The USS Enterprise arrives at a planet in the Omicron Delta system. Scans reveal the planet is friendly, but no animal or insect life exists. The crew is exhausted after three months of operations, so Captain Kirk announces shore leave for off-duty personnel, but first, he orders survey parties to scout the planet.

Dr. McCoy and Lt. Sulu make up one exploration crew. They discover a planet that is both stunning and tranquil. McCoy tells Kirk that he witnessed an anthropomorphic white rabbit, after which Alice from Alice in Wonderland inquired if a rabbit had just gone by. Kirk is suspicious that McCoy is attempting to convince him to take a break, even though Kirk had previously said he didn't require one. Officer Spock encourages Kirk to materialize on the planet's surface by stating that his physical health evaluation indicates his deteriorating performance.

Once Kirk and his aide Tonia Barrows have beamed down to the planet, McCoy presents Kirk with the footprints of a giant rabbit. In the meantime, Sulu discovers and uses a Colt Police Positive gun. Barrows reports that she was assaulted by Don Juan, with her uniform torn. Kirk is then briefly confronted by Finnegan, a cocky joker who pestered him during his time at the academy, and he meets Ruth, an ex. A samurai attack Sulu with a katana and mentions that his phaser failed to work. Kirk also discovers that his phaser is not functioning. Kirk commands a stop to the shore leave before any crew members have beamed down. Spock states that the planet radiates a force field siphoning energy from the ship's engines and obstructing communication. The energy patterns indicate industrial activity.

Spock transports himself to the planet's surface to acquire sensor readings. In contrast, the connection between the ship and the planet weakens, leaving Spock stranded with Kirk and the exploration teams without contacting the vessel. Subsequently, McCoy requests Yeoman Barrows to wear a medieval costume, and a knight on horseback charges at them. The doctor shields her, but the lance fatally spears him. Kirk shoots the knight using Sulu's pistol. Kirk and Spock examine the knight's body which is made of the same material as the planet's plants. A WWII fighter jet strafes the landing party, and during the chaos, the corpses of Doctor McCoy and the knight disappear.

Spock inquires Kirk about what he discussed before his "vision" of Finnegan. Kirk reveals that he was reflecting on his early days at the academy. Just as Spock anticipated, Finnegan reappears. Finnegan mocks the Captain before breaking for it, with Kirk chasing after him. They get into a tangle, and Kirk punches Finnegan out, something that he had always yearned to do. Spock and Kirk comprehend that their musings are causing their unreal encounters, though they are also becoming increasingly dangerous. Kirk orders everyone to cease pondering about anything.

An old man reveals himself to be the "Caretaker," and he explains that the planet is a kind of amusement park. There are no dangerous elements or long-term consequences within the park. Alongside him is Dr. McCoy, who was brought back to life due to the planet's influence. He introduces two Rigelian cabaret girls whom he thought of after being revived. The Caretaker apologizes for any confusion and extends the use of the planet's amenities to the Enterprise crew, warning them to be careful when making their choices. Captain Kirk approves the offer and allows the team to beam down, and Ruth appears again.