The Enterprise destroys the stolen space cruiser Aurora when it uses tractor beams to prevent it from entering Romulan space and the Aurora continues to use full power in an attempt to flee. The six passengers are beamed aboard the Enterprise before their ship's destruction, and prove to be Tongo Rad, the son of the Katulan ambassador (and must be handled with extreme delicacy because of ongoing Federation negotiations with Katula), Irini Galliulan (Chekov's former girlfriend and a Starfleet Academy dropout), Dr. Sevrin (a well-known research engineer in the fields of acoustics, communications, and electronics on from Tiburon), the musician Adam, and two unidentified girls. The group is dressed in far-out clothing, is disrespectful of authority, and calls Kirk ``Herbert'' (who was a minor official notorious for his rigid and limited patterns of thought---i.e., Herbert Hoover). The hippies demand to be taken to a planet called Eden and refuse to cooperate with Kirk. However, Spock seems to partially understand them when he makes a symbol and speaks of the ``One.'' As a result the hippies allow Spock to lead them to sickbay.
Medical examination of Sevrin reveals him to be a carrier of the synthecoccus novae virus and to be on the verge of insanity. Kirk orders Sevrin into isolation before he can endanger any crew members who may not have received complete vaccinations. The hippies object by calling Kirk ``Herbert'' again, and make up a protest song. Spock attempts to reason with Sevrin and offers to assist him in finding Eden and colonizing it, if he agrees to cooperate. However, Sevrin is so resentful of the impositions placed on him as a carrier of his disease (which has been created as a by-product of technological advancement) that he is oblivious to the damage he can impose on others and wants only to be free of the technology which his resulted in his infection.
Led by Sevrin, the hippies take control of the Enterprise by distracting crew members. Adam distracts Spock with music and arranges to hold a concert which is broadcast ship-wide (in which Spock joins in), and Irini distracts Chekov with love and finds out out to access the computer banks and navigate the ship. Finally, Tongo distracts Sulu with his hobby of botany. Tongo then knocks out Sevrin's guard and frees Sevrin, and the two up them knock out Chekov and take over the ship from auxiliary control and direct it toward Romulan space.
The hippies then complete Spock's search and find the planet they call ``Eden,'' which indeed lies in the Romulan sector. The hippies use hypersonics to incapacitate the Enterprise crew members and then proceed to land on the planet using the Galileo 2 shuttlecraft (NCC 1707/7).
Kirk manages to reach the auxiliary control panel and stop the sound. Kirk, Spock, Chekov, and McCoy then follows the hippies down using the transporter and find a beautiful planet. They quickly learn otherwise when Chekov's hands are burned when he touches a flower, and McCoy determines that all the plant life on the planet contains acid. The landing party discovers that Adam has been killed after eating appetizing-looking but deadly indigenous fruit. Sevrin refuses to leave and then deliberately eats a fruit which kills him. The landing party takes the remainder of the hippies (whose bare feet have been burnt) back to the Enterprise for medical attention.