The USS Enterprise responds to a distress signal for help. The away team, consisting of Captain Kirk, First Officer Spock, Chief Medical Officer Dr. McCoy, Yeoman Janice Rand, and two guards land on a planet that looks like it belongs in the 1960s on Earth. They come across a disfigured man who starts to have a fit and passes away when Kirk tries to protect them from him. They follow a sound to an empty building, where they find a young girl called Miri. She runs away because adults on the planet have been killing and hurting the children before they, too, die. Miri and her friends are the only survivors left. The distress signal the team followed is determined to be automated.

The exploration team, apart from Spock, observed purplish blemishes on their bodies; Miri informed them that these were the initial indicators of the sickness that had contaminated the planet, and they would soon become like the other grown-ups. Next, the group identified a scientific research lab and perused documents for hints to the illness, discovering that it was a consequence of a life-lengthening experiment impacting those who had achieved puberty; after a short period of frenzied madness, death followed. The "children" were indeed over 300 years of age, maturing one month every century, but displaying the psychological and passionate maturity of their appeared age instead of their actual age. When the sickness starts, its victims have a week to live. Although Spock seems immune, he regards himself as a bearer who could spread the contagion to the Enterprise if he returns.

Kirk attempts to convince Miri to direct him to the other kids, but they disperse when they sense his and Miri's presence. Jahn, the elder among them and the group's leader takes the touchdown team's communicators, making McCoy's quest to find a remedy futile unless they can access the Enterprise's computers. When Yeoman Rand gets frightened at the danger they face, and Kirk tries to console her, an envious Miri runs away and plans to take Rand captive with her confidants.

McCoy finds a potential solution to the virus. However, without the ability to measure the dosage, the remedy may be fatal. Kirk alerts Miri that they will contract the illness if they don't help him identify a cure. Knowing she is infected, Miri leads Kirk to where Rand is detained. Jahn then orders the children to swarm and confront Kirk. A wounded and bleeding Kirk pleads with the kids to think of their youngest, who will be helpless when the elders have perished. He points out that their supplies are running low; they will starve in six months. Finally convinced, Jahn gives the communicators back to Kirk. He gathers the kids and goes back to the lab. Nonetheless, in desperation, McCoy has already injected himself with the vaccine. The doctor's sores vanish, verifying the remedy's efficiency.
After everyone is vaccinated, Kirk sends word to Star Fleet to get the children on the planet help.