One of two newly discovered planets orbiting Kapteyn's star, just 13 light years from Earth, is ripe for life with just the right mild temperatures to allow surface liquid water.
But although a close neighbour, Kapteyn's star originated in another galaxy far, far away.
Scientists believe it was born in a dwarf galaxy that was absorbed and torn apart by our own galaxy, the Milky Way.
The surviving core of the dwarf remains in the form of Omega Centauri, a "globular cluster" of very ancient stars some 16,000 light years from the sun.
Astronomers have calculated that Kapteyn's star's planets could be 11.5 billion years old - more than twice the age of the Earth and only around two billion years younger than the universe itself.
One of the worlds, Kapteyn b, is five times heavier than Earth and orbits in the star's "habitable zone" where conditions are mild enough to permit watery oceans.
Whether life has evolved there remains open to speculation - but given the planet's age it could be far more advanced than on Earth.
Dr Guillem Anglada-Escude, one of the scientists from Queen Mary University of London, said: "It does make you wonder what kind of life could have evolved on those planets over such a long time."
The second planet, Kapteyn c, is more massive than its sibling and thought to be too cold to support liquid water.
Kapteyn's star, a "red dwarf" cooler than the Sun, was named after Dutch astronomer Jacobus Kapteyn who discovered it at the end of the 19th century.
It can be seen in the southern constellation of Pictor with an amateur telescope and sits in the "galactic halo", an extended cloud of stars orbiting the Milky Way.
Astronomers found the planets by using specialised instruments on telescopes in Chile and Hawaii to measure tiny "wobbles" of the star caused by their gravity.
Shifts in the "colour" of star light due to the wobbles allowed them to work out properties of the planets such as their masses and orbital periods.
"We were surprised to find planets orbiting Kapteyn's star," said Dr Anglada-Escude. "Previous data showed some moderate excess of variability, so we were looking for very short period planets when the new signals showed up loud and clear."
Details of the research are published in the journal Monthly Notices of the Royal Astronomical Society Letters.
US co-author Dr Pamela Arriagada, from the Carnegie Institution, said: "Finding a stable planetary system with a potentially habitable planet orbiting one of the very nearest stars in the sky is mind blowing.
"This is one more piece of evidence that nearly all stars have planets, and that potentially habitable planets in our galaxy are as common as grains of sand on a beach."
The discovery has inspired British science fiction author Alastair Reynolds to write a short story, Sad Kapteyn, which describes a robotic interstellar probe reaching the star's planetary system.
Mr Reynolds worked as an astronomer at the European Space Agency and later became a full time sci-fi writer.
The story can be read at www.http://ph.qmul.ac.uk/ancient-worlds-around-kapteyns-star