An Earth-like uninhabited planet in the Omicron Delta region seems the ideal location for rest and relaxation for the tired crew of the Enterprise. However, strange things soon begin to happen to the landing party. McCoy sees Alice and a white rabbit, Sulu finds an antique Police Special gun, Yeoman Barrels is accosted by Don Juan, and Esteban Rodriguez and Angela see birds. No one believes McCoy's Alice sighting until Kirk beams down and spots a giant rabbit track. Kirk cancels shore leave for the rest of the crew, but is then confronted with practical joker Finigan from Starfleet Academy on the one hand and his former girlfriend Ruth on the other. Meanwhile, Sulu has been attacked by a Samurai, Rodriguez and Angela have been confronted by a tiger, and Bones is making moves on Barrels, who has found princess's clothes.
Spock meanwhile reports from the Enterprise that he has detected a sophisticated power field on the planet which is draining the Enterprise's energy. Spock beams down to help investigate just as communications with the ship are becoming impossible. Pleasure over seeing Barrels dressed as a princess soon turns to terror when Bones is lanced by a knight. After bones is skewered, Kirk shoots the knight with the gun he has confiscated from Sulu. Investigation of the knight shows him to have the same cellular structure as the plants on the planet, and Spock surmises that it has been ``manufactured.'' Angela is then killed by a Japanese Zero airplane, and the bodies of knight and McCoy disappear.
After asking Kirk what he was thinking about prior to encountering Finigan, Spock realizes that the apparitions are being created out of the minds of the landing party. Upon thinking about the Academy again, Kirk conjures up Finigan and heads off on a wild chase after him. After Kirk catches up, Finigan lays him out flat. After more fighting, Kirk finally succeeds in doing something he had never done before, defeating Finney.
Suddenly, the planet's ``caretaker'' appears with a ``repaired'' McCoy (on the arms of two cabaret girls from Rigel 2). The caretaker apologizes for the misunderstandings and offers the services of the ``amusement park'' planet to the Enterprise's weary crew. Kirk accepts and authorizes the crew to beam down, but Spock has had his fill of shore leave and requests to be returned to the Enterprise.