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On the way to Starbase 10, the U.S.S. Enterprise stops to deliver supplies to the colonists of Gamma Hydra IV. A landing party consisting of Kirk, Spock, McCoy, Scott, Lieutenant Galway and Chekov beam to the planet's surface. They find that accelerated aging has taken place, killing most of the colonists. Chekov is terrified when he discovers the first body. The only survivors, an elderly couple who claim to be in their twenties, die shortly after meeting the Enterprise crew. When the landing party returns to the Enterprise, the aging acceleration begins to affect each of them ... except Chekov, who remains curiously immune. While Kirk wants to stay in orbit around Gamma Hydra IV until a cure can be found, one of his passengers, Commodore Stocker, wants to proceed to Starbase 10 where he feels the best medical aid can be obtained.

The senior officers succumb to the effects of old age and soon Kirk is unable to command, as are Scotty and Spock. Command falls to Commodore Stocker, who, while an efficient desk officer, has no deep space training. Thinking he will save time, Stocker plots a course through the Romulan Neutral Zone on his way to Starbase 10. The Romulans are waiting and begin an attack.

Stocker, panicked and inexperienced, has no idea what to do. As the Enterprise is surrounded, McCoy comes up with an antidote to the aging sickness ... adrenaline. Chekov, he explains, wasn't affected because his fear at finding the bodies on Gamma Hydra IV had already kicked his natural adrenaline into high gear.

McCoy restores Kirk to normal in time to save the ship by reusing his famous "corbomite" bluff and telling the Romulans that the Enterprise would destroy anything within a 200,000 kilometer radius. McCoy distributes the antidote and restores everyone to their normal state.