The Federation's spaceship Enterprise was instructed to reach out to a withdrawn species known as the Melkotians. As they drew nearer to the Melkotians' world, they encountered a probe that warned them to stay away. Team members heard the warning in their dialects, recommending that the Melkotians have telepathic capacities. Despite First Officer Spock's alerts about the ferocity of telepaths, Captain Kirk gave the order for the vessel to remain on its course. When they achieved orbit, Kirk, Spock, Chief Engineer Scott, Chief Medical Officer Dr. McCoy, and Navigator Ensign Chekov beamed down to the surface.

Upon arrival, the landing party is greeted by a delegate from Melkot, who informs them that they have been convicted of illegal entry. They then discover themselves in a bizarre vista resembling a traditional Wild West settlement, most of the structures just superficial wooden faces. Additionally, their phasers have been altered into six-shooters, and they cannot reach the Enterprise.

After wandering around the town, they discover a newspaper with the date October 26, 1881, the day of the famous battle at the O.K. Corral. The locals think that the landing team is the Cowboys:
Kirk is Ike Clanton.
Scott is Billy Clanton.
McCoy is Tom McLaury.
Spock is Frank McLaury.
Chekov is Billy Claiborne.
The team then finds out that some people wearing the Earp brothers' outfits, Virgil, Wyatt, and Morgan, as well as their deputy Doc Holliday, are getting ready to fight them at the agreed time.

Realizing that the gunfight had been fatal for most Cowboys in the past, the Enterprise personnel attempted to change their destiny by convincing the sheriff and the locals to terminate the fight and even tried to talk to the Earps, but their efforts were futile. At the same time, a barmaid named Sylvia drew close to Chekov, prompting the envious Morgan Earp to fire a shot that killed him. Spock remarked that the actual Billy Claiborne had made it through the incident, implying that today's events could have been altered in other ways. To that end, Spock made a makeshift tranquilizer gas grenade to try and subdue the Earps before the shootout, but he was surprised to find that the gas had no effect.

As the shootout approaches, Kirk and his crew are in the O.K. Corral when the Earps show up. Spock realizes this world is not governed by the same rules of reality and convinces the others that their faith in this fact will keep them safe. Kirk has Spock do a mind-meld with the rest of the team to ensure they are sure of this. So, when the Earps and Holliday fire their guns, their bullets go through without causing harm.

Kirk triumphs in a hand-to-hand fight with Wyatt Earp and takes away his firearm, yet when given the opportunity to exact retribution for Chekov, he throws away his weapon. The team and a still-alive Chekov find themselves on the Enterprise bridge (Chekov had been saved since his concentration was on Sylvia and not on the possibility of his death). The Melkotians communicate, ask about Kirk's reluctance to execute, and in the end, invite the Enterprise to approach their planet.