While on a mission to investigate a region of space in which starships have been disappearing at the rate of one every 27.346 years, the Enterprise is probed by a signal from the Taurean system — a signal which causes all the men aboard the ship to experience intoxicating visions of beautiful alien women and exotic locales. Kirk, Spock, McCoy, and security officer Carver beam down to the second planet in the Taurean system, where the women from their visions greet them. The women give the landing party food and drink, which turn out to be drugged. When Kirk and his officers awaken, they discover that their phasers and communicators have been taken, and that they have been fitted with jeweled metal headbands, which are causing them to age at a highly accelerated rate, rapidly draining away their life energies.

Back aboard the Enterprise, Uhura is alarmed by the behavior of the men in the crew, all of whom appear to have been intoxicated by exposure to the signal from the planet. Forced by these circumstances to relieve a lackadaisical Chief Engineer Scott and take command herself, Lieutenant Uhura makes Nurse Christine Chapel the starship's temporary chief medical officer. On the planet, the members of the landing party take doses of the stimulant cortropine from Dr. McCoy's medical kit in an effort to slow down the aging process. Spock, the least weakened of the team because of his Vulcan physiology, manages to get his hands on one of the communicators that their female captors had confiscated. Before the women render him unconscious and recapture him, Spock manages to contact the Enterprise long enough to make it clear to Uhura that the landing party is in dire need of rescue. Because no women have fallen victim to the strange signal from the Taurean world, Uhura organizes an armed, all-female team and leads it in an assault against the women on the planet's surface. Faced with Uhura's threat of destroying their temple with the Enterprise's phaser banks, the landing party's captors surrender, explaining that their race had fled to this world from their own dying planet, only to learn too late that the Taurean planet drains away the vital energies of humanoid life forms.

As the Taurean women are unable to leave the planet, they must recharge their depleted energies once every 27.346 years by luring passing starships to them and draining the men aboard of their life forces. At Spock's suggestion, the rescued landing party members use the molecular memory of the Enterprise's transporter to restore them to their normal ages, and Kirk agrees to use his starship to relocate the Taurean women to a more suitable planet.