The U.S.S. Enterprise is in pursuit of a stolen star cruiser, the 'Aurora', which is heading directly for Romulan space. Under the strain of the chase its engines start to overheat and the six occupants are beamed aboard the Enterprise just before the craft explodes. Kirk and Spock head towards the transporter room, having been advised by Starfleet that one of the group is Tongo Rad, who is the son of the Catullan ambassador with whom they are currently in delicate treaty negotiations, and that the group should be dealt with tolerantly.

The leader of the group, who have the appearance of 20th century 'hippies, is a man called Dr. Sevrin who used to be a brilliant research scientist in communications and acoustics on the planet Tiburon. Their philosophy of 'One' is symbolised by an egg shape which they make with their hands which Spock appears to understand as it has similarities with his own IDIC beliefs. Spock explains to Kirk that the group has rejected the use of modern technology, returning to more primitive basics, and is searching for a paradise world that they call 'Eden'.

McCoy gives them a routine medical check-over and discovers that Sevrin is a victim of the technological society that he has forsaken and is a carrier of the artificial virus synthococcus novae, which could prove potentially deadly to undeveloped planets. Despite his followers protests Sevrin is put into isolation by Kirk which results in the captain being branded a 'herbert' because of his being a stickler for regulations. Spock tries to reason with Sevrin about his condition but concludes that the man is insane. However, the Vulcan becomes curious about their quest and carries out his own researches into the possible location of 'Eden'.

The rest of the group are allowed to mix with the ship's crew and are impressed by Spock's virtuosity with the Vulcan lyre when he takes part in a 'jamming' session. Chekov discovers that one of the group is a girl called Irina Galliulin with whom he had a relationship before they fell out when she dropped out of Starfleet Academy. Sevrin is 'rescued' from his isolation by Tongo Rad and the group makes its way to an auxiliary control room where they manage to gain control of the ship. Using the results of Spock's research and calculations they plot a course towards 'Eden' which takes them directly through Romulan space. On arrival, Sevrin uses his knowledge of acoustics to render the crew of the Enterprise unconscious and his group travels down to the planet's surface in a shuttlecraft.

On regaining consciousness, Kirk takes Spock, McCoy and Chekov down to the planet where they discover that the plant life, although beautiful, is acid-based and deadly. The group of six are found sitting in the shuttlecraft, nursing burns to their bare feet caused by the acidic grass. Sevrin's insanity comes to the fore and, disregarding the intense pain, he runs to a tree and takes a bite out of one of its acidic fruits which kills him instantly. The rest of the group are taken back on board the Enterprise and delivered to the nearest starbase where the various characters make their farewells and Spock expresses the hope that they will one day discover the 'Eden' for which they are searching.