While en route to Babel transporting Commodore Robert April, the U.S.S. Enterprise's first captain, and Dr. Sarah April, his wife and ship's first doctor, the Enterprise inadvertently locks a tractor beam on a ship diving into the Beta Niobe Nova. Both ships plunge through the nova and into a bizarre parallel universe where everything is backward. With time flying in reverse, the crew begins to grow younger at an accelerated rate.

Backtracking a mysterious alien probe, the U.S.S. Enterprise encounters a ship in the shape of a giant feathered serpent, which turns out to be Kukulkan, a god of ancient Mayan-Aztec legend. Its captain, Kukulkan, is actually a very long-lived benevolent entity who wants the humans to worship him just as the Mayans and Aztecs did. He insists on putting Kirk and others through a test to determine if they have grown sufficiently to receive his wisdom.

The U.S.S. Enterprise goes to the planet Dramia to deliver medical supplies, only to have McCoy arrested and put on trial for deliberately spreading a plague that killed most of the population of the colony Dramia II. Nineteen years earlier, Dr. McCoy headed a mass-inoculation program there against Saurian virus. This disaster occurred after his team left the planet. Now Kirk must clear his friend's name before the doctor is executed.

After avoiding a Romulan ambush by three of their warships, the U.S.S. Enterprise enters a strange energy cloud. The gaseous cloud affects the ship's computer turning it insane. With the crew at the mercy of the Enterprise's computer, it indulges in a series of increasingly aggressive practical jokes.

The U.S.S. Enterprise hosts Commander Ari bn Bem, an arrogant member of a neutral race from the newly-contacted planet Pandro. However, Bem endangers all of their lives when he conducts a test of suitability upon Kirk and Spock during an exploratory mission. This occurs on a planet of primitive natives under the guardianship of a noncorporeal being.

Spock is stricken ill with a disease that is fatal to Vulcans. With time running out, the U.S.S.Enterprise must rendezvous with the S.S. Huron, a freighter carrying the only known antidote. However, Orion pirates hijack the shipment and Kirk must deal with them before Spock dies.