A U.S.S. Enterprise landing party beams down to an uncharted planet. The planet seems like a perfect candidate for shore leave with its "Earth-type" characteristics. Kirk sends McCoy down with the party to check it out.
McCoy's first encounter on the new world is with a life-sized white rabbit in a waistcoat, being chased by a little girl in a pinafore. Kirk answers McCoy's somewhat odd call for help and beams down himself to find his old rival from his academy days, Finnegan. While trying to catch his old enemy, Kirk meets Ruth, an old girlfriend. He notices that neither Finnegan nor Ruth have changed in appearance since he's last seen them. Elsewhere, Sulu is attacked by a Samurai Warrior while others are chased by tigers and aircraft.
McCoy, who has paired off with Yeoman Tonia Barrows, is killed by a black knight on horseback. As the perils become more and more deadly, Kirk and Spock realize that their thoughts are somehow coming to life around them.
An old man appears, explaining that this planet is designed as an "amusement park," and he is the Caretaker for the world. The planet is not meant to be hostile, and the results of one's fantasies are not lasting. McCoy appears, healed, with a Rigel Cabaret girl on each arm. Tonia disengages the good doctor and they go off to spend what promises to be an enjoyable vacation together. The Caretaker invites Kirk and his crew to spend their leave on his planet. Kirk agrees, realizing that once warned, it would provide a most diverting vacation spot. As he makes his decision, Ruth appears.