When Chekov, Spock, Lt. Gallway, McCoy, Kirk, Scotty beam down to resupply the experimental colony on Gamma Hydra 4, they initially find no one home. Kirk is puzzled since he had just talked to the leader of the expedition an hour earlier. Stranger still, Chekov finds a dead man (Alvin) in one of the colony's buildings who appears to have died of old age. However, Spock maintains that this cannot be true because the expedition was composed of only young people. The leader, Robert Johnson (age 29) then appears, along with his wife Elaine (age 27). Both appear to be extremely old.
Kirk beams the landing party up together with those of the colonists who are still alive. Aboard the Enterprise, the colonists die of old age. Kirk puts Spock, Commodore Stocker (who is on his way to Starbase 10), and his former flame (of 6 years, 4 months, and some odd days) Dr. Janet Wallace on the investigation team. The only unusual event which Spock can determine is that an unusual comet passed by the planet shortly before.
Kirk then begins to lose his memory and displays advanced arthritis. Scott, McCoy, Lt. Gallway, and Spock also show signs of aging (at a rate of 30 years per day), but Chekov curiously does not. Spock then finds the source of the affliction. Apparently, the comet whose tail Gamma Hydra 4 passed through (and is now in quadrant 448) is emitting low energy radiation. Commodore Stocker becomes increasingly concerned about Kirk's condition, and forces Spock to hold a competency hearing. Meanwhile, Lt. Gallway dies of old age and Chekov continues to remain unaffected.
Kirk is found incompetent, and Commodore Stocker takes over. He orders the Enterprise to head directly for Starbase 10, through the neutral zone. Meanwhile, McCoy and Kirk realize that the one difference between their experience on the planet and Chekov's was that Chekov was scared to death upon encountering the dead body. McCoy recalls that early investigations showed adrenaline to be a potentially useful drug from combating radiation, although it was subsequently abandoned when hyronaline was discovered. Spock develops an injection containing adrenaline, which he first tries on Kirk. Fortunately, the shot is effective, and Kirk is able to assume control of the Enterprise, which is now under attack by the Romulans thanks to Stocker's incompetence in violating the Neutral Zone.
In a clever subterfuge, Kirk transmits a message using Code 2, which has been broken by the Romulans. He claims that the Enterprise has inadvertently strayed into the Neutral Zone. Kirk also claims he will destruct the Enterprise using a corbomite device which will destroy everything within a 200,000 km diameter, and that the explosion area will have to avoided for 4 years. The Romulans give a little ground lest they be destroyed in the upcoming explosion, and Kirk immediately races out of the Neutral Zone and into Federation space at Warp 8.