Dr. McCoy discovers he is dying and finds that an asteroid is actually a generational ship.
McCoy learns that he has a fatal disease, and then the Enterprise finds an asteroid heading for a populated planet. The asteroid is actually a giant ship, the Yonada, whose people have forgotten that they are travelling and believe it to be a world. McCoy falls in love with their priestess, Natira.
The story focuses on McCoy and the question of what he wants to do with the time he has left. It also addresses a lost people living by an old religion. Fans remember it for DeForest Kelley's performance and for the generational ship concept, a classic science fiction idea.