As a young actor in the 1960s, he was appearing on stage in a New York theatre next door to where Fiddler On The Roof was playing. Glaser happened to be dating one of the cast members and each night, once his show had finished, he would rush next door and watch the last five minutes of the musical.
A few years later, Glaser's first film role came in Norman Jewison's 1971 big screen adaptation of the Russia-set show. Fiddler On The Roof - written by Jerry Bock, Sheldon Harnick and Joseph Stein - saw Chaim Topol recreate the lead role of Tevye the milkman, which he first played in the 1967 West End production following Zero Mostel's turn on Broadway.
Glaser played Perchik, the Bolshevik revolutionary who falls for one of Tevye's five daughters. Now, 42 years on, Glaser is stepping into Topol's shoes to tackle the role of Tevye in a new touring revival that arrives in Edinburgh this week.
"He is a wonderful character to play," Glaser says, "and it is one of the better roles out there. He is an everyman, and we can all find bits of ourselves in him, dealing with changes and everything else that goes on in the world. He is a lot of things: he is a father; he is a learner, who has this tremendous curiosity and a thirst for knowledge; he is a bit of a clown, a bit of a fool. There are so many qualities of all of us in him."
Having worked alongside Topol, Glaser is unequivocal in his praise for the man whom many see as having defined the role of Tevye.
"He was a force of nature," says Glaser. "It was my first film, so I was totally new to the experience, and had so much to learn. Topol had been very successful doing the show on stage, and he was very striking to watch. He very much made the role his own, and I hope I bring something of myself to the role as well."
In between Glaser's associations with Fiddler On The Roof has been a chequered career on stage and screen, as well as a personal life marked by tragedy. Glaser remains best known for his role as Starsky in seminal 1970s TV cop show, Starsky And Hutch. The programme, about a pair of very cool detectives, transformed the careers of both Glaser and his co-star David Soul.
While his on screen other half Soul went on to have a pop music career on the back of the success of the series, Glaser ducked the limelight and gave up acting for a decade to direct films, including The Running Man, starring Arnold Schwarzenegger, as well as episodes of Miami Vice and other television shows.
Glaser seems reluctant to talk about his time in Starsky And Hutch these days. All he will be drawn on, in fact, is that he remembers those days "with a faulty memory and impaired vision".
Of his move back into acting, Glaser says that "After I directed five feature films, I became uncomfortable with the video system, and I decided I wanted to write, and I started a screenplay that became a book."
That book was Chrystallia And The Source Of Light, a children's novel that reflected some of Glaser's concerns beyond his career. In 1981, his wife Elizabeth contracted HIV from a blood transfusion she had while giving birth to the couple's first child, Ariel. This was not diagnosed until four years later, by which time both Ariel and the Glasers' second child, Jake, had also been diagnosed HIV positive. Ariel died in 1988 and Elizabeth in 1994, after founding the Elizabeth Glaser Pediatric AIDS Foundation.
"The book is kind of a metaphor for my life," Glaser says. "It's about a 14-year-old child whose mother is dying, and a little boy who needs to believe in something. Some adults like it, and adults who don't like it are those who don't like to live with the presence of fear in their lives. That is what the book is about. It is a fantastical adventure that asks what is the purpose of fear in our lives."
Despite the seriousness of the book's themes, Glaser does not see it as a purging for him. "It's a reaffirming," he insists, "and every time I talk about it, it's a reaffirmation."
Glaser was born in Cambridge, Massachusetts, in 1943, and studied English Literature before graduating with a master's degree in Theatre.
"I don't know how I became an actor," he reflects. "My mother was always encouraging me to perform, and one of my two older sisters was always into performing, so that may have been an influence."
Glaser worked in rep in New York, gradually picking up small TV roles, "doing a soap opera in the daytime, and a Broadway show at night." Now 70, Glaser's advice to younger actors starting out is simple.
"Don't," he says. "Not unless you have a need to do it. If you really want to be an actor, go to a big city, whether it is London, New York or wherever, do what you have to do to survive, and see if you can get through it. If it is just about ego, then you're asking for trouble.
"When I was younger, I used to worry, and think, 'God, I hope I get that part', but I don't do that any more. Some time ago I had just done a job on a TV show, and I realised I had not only had a good time, but that I had created that good time for myself. For me, acting, like all the creative arts, is a journey of self-discovery. What drives me is what drives you and what drives us all. We are looking for some kind of peace and fulfilment, and a sense of oneness with the world."
Fiddler On The Roof, Edinburgh Festival Theatre, October 1-5. In Conversation With Paul Michael Glaser: A Life On Stage And Screen will take place at Edinburgh Festival Theatre on October 4 at 3.30pm as a fundraiser for Scotland's HIV charity Waverley Care.