The Enterprise has been assigned to assist with the evacuation of the remaining inhabitants of a planet called Sarpeidon whose star, Beta Niobe, is due to go nova in a matter of hours but sensors indicate only a single life form on the planet. Kirk, Spock and McCoy beam down to investigate, materialising in what appears to be a library of some sort. The three of them are greeted by an elderly man called Mr. Atoz who initially makes the mistake of thinking that they are late arrivals from among the planet's inhabitants.

After being told differently, he explains to them that he is the librarian and claims to have sent Sarpeidon's population to safety into the planet's past by use of a machine called the atavachron. The Enterprise men start to examine some disks that show different periods of the planet's past. Kirk is looking at an era that bears a resemblance to 17th century Earth when he hears a scream coming from the archway of the atavachron. He immediately races through to assist, despite protests from Atoz, and finds himself in the period of history that he had been viewing. Spock and McCoy follow close behind him but they had been viewing a different set of disks and find themselves trapped in the planet's ice age.

Kirk rescues the woman he heard screaming from her attackers but she becomes frightened when she hears him talking to 'demons' Spock and McCoy through the time portal and has him arrested for witchcraft. In the ice age McCoy collapses from the cold, but he and Spock are found and rescued by a fur-clad woman called Zarabeth. She takes them back to her cave where McCoy recovers. Zarabeth tells them that she is alone, having been exiled there by an evil tyrant called Zor Khan after her family plotted against him. She also explains that the atavachron changes them physically when they pass through the portal and it is now impossible for them to go back as they will rapidly age and die.

At Kirk's trial for witchcraft the prosecutor turns out to be one of the time travellers and he helps Kirk to get back to the portal and return to the library. Despite there being many identical replicas of Atoz in the library, Kirk manages to locate the real one and forces him to find the disk that Spock and McCoy were viewing before they disappeared. Zarabeth eventually decides to reveal to McCoy and Spock that it is only herself who cannot return through the time portal as she has been 'processed' whereas they have apparently not. She admits that she had only tried to keep them there to save herself from the loneliness.

They make their way back to the area of the portal where they hear Kirk's voice calling them. Although Spock, who has started to display emotions like his ancient ancestors, is reluctant to leave Zarabeth, he realises that he must and they both step back through the portal into the library where they find that time is running short. Atoz grabs the disk of the time he has chosen for himself, places it in the machine, and races past them into the atavachron. The landing party is beamed back aboard the Enterprise which manages to get to a safe distance in time to avoid the effects of the nova which obliterate the planet.