The USS Enterprise, while transporting Commodore Stocker to Starbase 10 for his new command, makes a stop at Gamma Hydra IV to resupply a research station. A landing party, including Captain Kirk, First Officer Spock, Dr. McCoy, Chief Engineer Scott, Ensign Chekov, and Lieutenant Galway, beams down and discovers a deserted station with a dead older man. They encounter Robert and Elaine Johnson, who appear 50 years older than their actual age, and soon die in the ship's sick bay.

Spock and Dr. Janet Wallace investigate the mysterious aging, linking it to a recently-passed comet emitting low-level radiation. The landing party, except for Chekov, begins aging rapidly, with Lt. Galway dying first. As Kirk's memory deteriorates, he inadvertently uses an obsolete code, leading to a hearing where he is deemed unfit for command. With Spock also affected, Stocker directs the ship through the Romulan neutral zone.

Kirk, McCoy, and Spock consider Chekov's immunity, theorizing that his adrenaline levels protected him. Spock, Dr. Wallace, and Nurse Chapel develop an adrenaline-based treatment. As the Enterprise enters the neutral zone and comes under attack from Romulan vessels, Stocker falters. Meanwhile, Kirk insists on testing the drug in the sickbay, which successfully reverses the aging process. He then rushes to the bridge to take command.

Kirk outmaneuvers the Romulans by sending a message using the broken code, threatening to self-destruct the Enterprise with the "corbomite device," which would also destroy nearby ships. The Romulans retreat, allowing the Enterprise to make a surprise escape.