Remarkably, four years ago, Jessica Chastain was all but unknown.

"Doesn't it feel like a lot longer?" she remarks. "It feels like it was 10 years ago for me. I've done, like, 300 films, right?" She's joking - but only just. Since starring in Terrence Malick's The Tree of Life, giving an evocative turn as a grief-stricken mother, the red-haired starlet has been on an intense ride: roles for everyone from Al Pacino to Christopher Nolan, two Oscar nominations and a place on Time magazine's list of the 100 most influential people in the world.

Head-spinning isn't the word; all of a sudden, Chastain was being greeted by her idols, embraced as one of their own. "I remember I met Gary Oldman on the red carpet," she recalls. "I was so excited to meet him. And he had seen my films! That was a huge shock to me. It wasn't the kind of conversation I imagined having with someone who I had so much respect for. I thought it was going to be like, 'You're amazing!' And we'd talk about all the movies of his that I'd seen. But then he started speaking about my performances. It was very exciting."

Nominated in 2012 for a Best Supporting Actress Oscar for her sassy southern belle in hit movie The Help, a year later she was back again - this time as a Best Actress nominee for her stunning turn as a CIA agent on the hunt for Osama Bin Laden in Kathryn Bigelow's Zero Dark Thirty. In January that year, Bigelow's film had debuted at number two at the US box office. And number one? It was horror film Mama, also starring Chastain. It was the first time in more than 50 years that a leading lady had taken the top two spots in the charts.

Admittedly, it had been a long time coming. After making her feature film debut in 2008's Jolene, she spent three years filming a series of roles that, for one reason or another, were delayed. While Malick took an eternity cutting The Tree of Life, John Madden's The Debt was held in limbo due to studio politics. Meanwhile, Al Pacino's 2011 documentary Wilde Salome has struggled to get a cinema release, only premiering at London's BFI last year shortly before Chastain was glimpsed in Nolan's sci-fi opus Interstellar when she played the adult Murph, McConaughey's daughter.

When we meet, it's at a beachside restaurant in Cannes, the scene of Chastain's remarkable breakthrough in 2011, when she was nervously escorted up the red carpet by Brad Pitt and Sean Penn, her co-stars in The Tree of Life. With her that year was her actress-friend Jess Weixler, whom she met at the New York drama school Julliard. Chastain had supported Weixler when her movie Teeth hit the Berlin Film Festival; Weixler returned the gesture, even helping her into her dress and videoing her red carpet moment with a smartphone.

"I was so inspired to watch her become a movie star in that moment," Weixler tells me later, admitting it's been "crazy" watching her friend's life transform. "The time we have now to hang out now is much more precious. But I'm so proud of her that she's handling it as gracefully as she is. She's super-grounded. I think it helps when you come into it and you've already been studying it [acting] for a long time. You're a little more in your own skin as a person."

This is certainly true. Chastain, 37, doesn't seem to have changed a jot from her early years in Hollywood. Polite and humble, while she's no hermit, she's kept celebrity at bay, partly because for the past three years she's been on set making back-to-back movies. "I don't really feel a big change," she says. "I'm not incredibly exposed. My private life ... I'm still able to keep it private. Whatever people read about me usually has to do with my work, and because of that I don't get people chasing me."

She calls herself a "shadow-whisperer", hiding in the darkness, rather than making sure she's in the glare of the flash bulbs at some fashionable night-spot. "She's not out there clubbing with [Justin] Bieber - though she never would've been," laughs Weixler, who moved in with Chastain in their second year at Julliard after both found their dorm-room accommodation too noisy. A party animal she is not, it seems. "I'm not a big drinker," confirms Chastain.

Looking demure with green feline eyes, she's sitting wrapped in a blanket, sheltering her pale skin from the breeze coming off the sea. Sipping lemon tea, it's the night after the premiere of The Disappearance of Eleanor Rigby, one of several new films due out this year in which she appears. Later tonight, she'll wow the onlookers again in a sensational midnight-blue Atelier Versace gown, demonstrating the sort of effortless elegance and old-school Hollywood glamour that seem to come naturally to her.

This morning, however, she's dressed in a beige floral-embroidered Dolce & Gabbana mini-dress and a pair of vertigo-inducing Louboutin heels. Not very practical but it's not Chastain's regular attire. These are rare occasions, and Chastain admits embracing the glamorous side of her profession has been strange. "I haven't gone: 'Yeah, this is my life!'" she says. "Every once in a while, someone will come up and say nice things about a film I'm in, which has been really good."

The last time I saw Chastain, it was at the previous Cannes when she was sitting in the audience for the premiere of All Is Lost, JC Chandor's remarkable film starring just Robert Redford as a solo sailor in jeopardy. Chastain wasn't connected to the film but she was sent an invitation and, as a fan of Chandor's debut, the dialogue-driven Wall Street drama Margin Call, she was intrigued enough to go. "I thought: 'I'm going to go to this because he's one to watch.'" Briefly meeting afterwards, she laid her cards on the table. "I said, 'I just want to work with you.'"

Her instincts served her well and he immediately sent her the script for his third film, A Most Violent Year. It's already gained her a Best Supporting Actress nomination at the Golden Globes - a prize she won for Zero Dark Thirty - and a third Oscar nod in four years looks distinctly possible. Meanwhile, the film's Best Picture triumph at the National Board of Review, where Chastain also claimed Best Actress, puts it as a possible Academy Award contender.

The film casts her alongside fellow Julliard alumni Oscar Isaac, who was so good in last year's Inside Llewyn Davis as the troubled folk singer and is soon to be seen in the new Star Wars movie. It was Chastain who suggested Isaac when Javier Bardem, the original actor lined up, dropped out. "Immediately I was like: 'Oscar Isaac.' Jess and I went to Julliard with him [though Isaac was several years below them]. He's perfect for the role. He's so talented. He was amazing in Inside Llewyn Davis. And I'm really excited for everyone to see his performance."

Playing Anna Morales, wife to Isaac's oil baron husband Abel, she and Isaac make for a fine screen pairing in an absorbing story set in a wintry Big Apple in 1981 - "one of the most violent years in the history of New York", explains Chastain. A tale of characters desperately clinging to the American Dream as if it were a life-raft, the story revolves around Abel's business, which is hanging by a thread as an unidentified rival is hijacking his tankers.

Chastain's Brooklyn-raised character is unlike any other she's played. "She's, like, nouveau riche and very much a daddy's girl," she says, and there's a vampy quality to her - blonde hair, claw-like nails, thick red lipstick and a no-nonsense attitude. Yet there's more to Anna than merely criminal arm candy. On some level, she's complicit in her husband's shady dealings. With "more authority" than Diane Keaton's character in The Godfather, "she knows what she's doing", says Chastain.

It was a trying shoot for the actress, not least because she was shuttling back and forth between Chandor's film in New York and Guillermo Del Toro's new 1901-set mystery Crimson Peak, which was filming in Toronto. "That was tough, having to fly from set to set, and do two different accents." She grimaces. "I'm never doing that again." It seems she's spent most of her time in hotels and airport lounges these past months. "Which is not so much fun," she admits. "But I have my dog companion, Chaplin, who travels with me."

There is a human companion too, Gian Luca Passi de Preposulo, an Italian fashion executive currently based in Milan. As part of her policy to keep her private life just that, Chastain has maintained a dignified silence around their relationship ("I won't talk about my love life until I'm engaged," she has said). While she had been based in Venice Beach, California, for a time, she's now moved back to New York, which makes swift red-eye hops to Italy more practical.

They've been together since June 2012, after reputedly meeting at a Paris fashion show. She breaks into a little Italian, proving that communications between the couple aren't all in English. "I had very good teachers - Claudio and Fabiano!" she beams, pointing out that she learned in Milan at the Scuola Leonardo da Vinci. It seems apt, somehow, that Chastain should be dating a European, for she comes across as an actress who, once upon a time, would've flourished on the continent.

As if to prove this, she recently completed Miss Julie, a new film adaptation of the classic August Strindberg play directed by Liv Ullmann, the one-time muse for Sweden's legendary Ingmar Bergman. "She's the most sensitive and open person I've ever known," says Chastain, who plays the title role, the daughter to a wealthy baron who becomes embroiled in an affair with her father's valet (Colin Farrell). "There's something very beautiful about her [Ullmann]: no matter what, she leaves herself open. It's a risk she's willing to take."

Still, as European as she might seem, Chastain's own upbringing was very blue-collar American. She was born Jessica Howard (later taking her mother's maiden name) in Sacramento, California, the eldest of five. Her father Mike is a fireman and her mother Jerrie a stay-at-home mother, and she remains close to her family and protective of her younger siblings, whose friends for a long time didn't even know about their older sister's Hollywood career. "It's been very important to my family to keep it private," she says.

Not that Chastain has shut her family out from her success; far from it. When she first went to the Oscars, she took her grandmother with her "as my date". She smiles at the memory. "It was wonderful to see it through her eyes. I kept looking over at her, and her mouth was open the whole time. She was so excited, and told me it was the best day of her life. It was really emotional for me to share that with her. It's a moment I'll remember for the rest of my life."

When she was seven years old, Chastain's grandmother took her to see a touring production of Joseph and the Amazing Technicolor Dreamcoat, starring David Cassidy. School had never been her thing, but watching that play, which had a young female narrator, similar to her age at the time, was revelatory. "That was a complete 'a-ha' moment for me," she says. After that, she was hooked. "The whole time growing up, I said I was going to be an actor and everyone [in my family] was like: 'We don't know how this is going to happen, but OK.' They were cool with it."

She spent her teenage years performing in amateur Shakespeare productions around the San Francisco Bay area, and after playing the female lead in a well-liked production of Romeo and Juliet, she was encouraged by another cast member to audition for Julliard. Winning a place at the prestigious academy, and using a scholarship that had been provided by another alumnus, the late actor Robin Williams, Chastain was on her way - the first in her family ever to go to college.

Chastain's early days in LA were tough: casting directors rejected the 5ft 4in actress because she wasn't blonde or tanned. "I looked very different - and they said I looked like I was from another time." But winning bit parts on such shows as ER and Law & Order, as well as a 2005 TV movie version of vampire show Dark Shadows, kept her from giving up. About a year later she got a call to audition for Pacino's Los Angeles stage production of Oscar Wilde's play Salome. With her performance also filmed for Pacino's behind-the-scenes doc, Hollywood immediately took notice - and it hasn't stopped taking notice.

Currently filming The Martian, Ridley Scott's new film, Chastain is in almost constant demand, though she hasn't forgotten her indie roots. The Disappearance of Eleanor Rigby is a prime example. Starring Chastain and James McAvoy in a story about how a couple deal with themselves and each other after the death of their infant son, it's boldly experimental, shot across two films - subtitled Him and Her - that show both perspectives. "It's unlike anything I've done," she says.

Chastain loved working with McAvoy. "He's so cool, so easy, so warm, funny, like a normal guy. I love his loyalty. He's a good family man. And he's super-talented. Being able to just respond to what he was doing was really exciting. He would invent things. He would crack jokes in the middle of a scene, which would sometimes be tough for me, because Eleanor would respond differently than I would to a joke in a certain moment. But he always kept it light, which I think was important for this material."

While McAvoy is a father, Chastain has yet to have children. "It's interesting, because Eleanor, when we meet her, has been denied being a mother at this point in the story. She's already suffered her great tragedy, and she's trying to figure out what to do with her life." Does she think about having kids herself? She nods, carefully. "I've always wanted to be a mom, and I hope to be a mom some day. And many of my friends tell me I mother them now!"

She might have to slow down her phenomenal work-rate if she wants to become a parent, a difficult prospect when she's one of the few actresses being offered fully-rounded female roles. She has a beef with most of the scripts she sees. "Most of the time when there's a woman on screen she's talking about a man." This, understandably, does not make her happy. "Women are half the population, and we need to include that half of the population more." Like her Twitter page says: actor, bookworm, feminist, Elvis fanatic, friend of animals everywhere.

A Most Violent Year (18) is in cinemas now. The Disappearance of Eleanor Rigby, Miss Julie and Crimson Peak will be released later in the year.