The U.S.S. Enterprise intercepts a stolen Federation shuttlecraft which contains a humanoid named Lokai. Taken aboard the ship, Lokai tells the crew he is from the planet Cheron, and asks for asylum on the U.S.S. Enterprise. His most distinctive feature is that he is half black and half white, starkly separated down the middle of his body.
The U.S.S. Enterprise tracks another vessel, pursuing at great speed. The ship's only passenger beams on board and is discovers to be another humanoid from Cheron. The difference in this man, Bele, is that his black and white skin is reversed from Lokai's. Bele claims to be Cheron's chief officer sent out to bring in political traitors, and has been pursuing Lokai. The more the two men are aboard the starship, the more Kirk realizes that the basic problem between them — and their entire race, apparently — is their opposite color. Tiring of their bigotry, Kirk decides to ignore the two guests and concentrate on his original mission; to decontaminate the planet Ariannus, plagued with a bacteria that endangers billions of lives.
When Bele takes control of the U.S.S. Enterprise in a desperate attempt, Kirk sets the ships auto-destruct sequence instead of allowing the hijacking to continue, and the alien returns command to the captain. However, once planet Ariannus is decontaminated, Bele takes back his control over the starship and leads it back to Cheron. What they find is a long-dead planet, annihilated by their interracial bigotry. Lokai beams down to the surface to escape Bele, who follows. The U.S.S. Enterprise leaves them on the surface, to decide their own fates.