When the Enterprise responds to a distress signal from a planet (which just happens to look exactly like Earth: mass: 6 x 1021 tons, density 5.517, circumference 24,874 miles, oxygen-nitrogen atmosphere), Kirk, Spock, Yeoman Janice Rand, McCoy, and two security guards beam down and find a copy of Earth in the mid-1960s. On the planet's surface, while inoffensively examining a tricycle, they are attacked by a creature clad in rags. The creature appears to be a disfigured human, but with an extremely accelerated metabolism. He dies shortly after the encounter, but a security guard spots another inhabitant. Following it into a building, the landing party finds a 300-year old piano. They also discover their quarry to be a young girl named Miri. Miri is afraid of the landing party because they are ``grups,'' and the grups killed and hurt children before themselves dying.
The members of the landing party soon learns that they are all infected by a strange disease which causes death to anyone who has reached puberty. At a deserted hospital, they discover that the disease with which they are afflicted (which causing blue rashes) was accidentally created by a project to prolong life. They also discover that the ``lonelies'' (children) on the planet are actually over 300 years old, having aged only one month for every hundred years of real time.
Kirk is attacked by Louise, a girl who has just gone through puberty, and stuns her with a phaser. Like the first creature, she dies. The landing party find old records and discovers that they have only 7 days to live. Meanwhile, the children, led by Jahn, steal the landing party's communicators, rendering their search for a cure almost impossible. When Janice becomes upset and Kirk hugs her to comfort her, Miri becomes jealous and runs away to scheme with the rest of the children. Together, the children devise a ``foolie'' which consists of kidnapping Janice.
Kirk tries to convince Miri that all children eventually contract the disease, despite her protestations that it only happens ``sometimes.'' Miri takes Kirk to the children who proceed to attack him. After Kirk has shown them that it is they who are doing the hurting, and convinced them that they will die without his help, the children finally listen to the ``grups.'' Kirk returns to the hospital, only to find that Bones has injected himself with a possible vaccine. Fortunately for Bones, the vaccine is found to be safe and effective, and all are inoculated. They leave the children behind and contact Starfleet to send advisors and teachers.