The crew of the Starship Enterprise, composed of Captain Kirk, First Officer Spock, and Chief Medical Officer Dr. McCoy, teleports down to a planet in response to emergency communication. Upon arriving, they are welcomed by an amiable small person named Alexander (Michael Dunn). He takes the landing group to meet the remaining members of his group, who have adopted the traditions of ancient Greek culture and have named themselves Platonic in honor of the Greek philosopher Plato.

All the Platonians except Alexander have psychokinetic abilities, and the ruling class has grown haughty because of it, feeling that they can do whatever they want. They explain to the Enterprise crew that they "deceived" them into going to their planet because their leader, Parmen, needed medical attention. After being tended to by Dr. McCoy, Parmen orders him to stay on the planet to treat other Platonians too. When Captain Kirk speaks against it, the Platonians use their supernatural powers to punish him.

Alexander is afraid to tell Spock and Kirk that Parmen desires to kill them.

Parmen continues to degrade Kirk and Spock in front of Dr. McCoy, hoping to persuade them to stay on the planet. Subsequently, the Platonians use their powers to bring two other crew members of the Enterprise to the planet for their pleasure: Uhura, the Communications Officer, and Nurse Chapel.

McCoy takes a sample of Alexander's blood and manages to locate the kironide mineral responsible for providing the planet's people with exceptional abilities; it is plentiful in the local food and water sources. McCoy can mix up a serum and inject Kirk and Spock with doses that will give them double the might of Parmen. Alexander inquires as to where Kirk is from and if size matters. Kirk answers that size, color, and species are not necessary. Alexander implores them to accompany Kirk.

As Kirk and the others waited for the serum to start working, Parmen forced them to perform a show again. However, Alexander became furious after seeing the Platonians ridiculing the crew, and he attempted to stab Parmen with a knife, though he failed.

After Kirk uses his newfound abilities to control objects with his mind to overpower Parmen and spare Alexander's life, Parmen pledges to end his intimidating behavior. Nevertheless, Kirk does not believe him and cautions that if Parmen goes back on his word, anyone can recreate the same powers to control him.

Kirk commits to sending the appropriate medical staff to the planet on the condition that the Platonians are obedient. Alexander desires to travel with the Enterprise to initiate a new existence in another part of the universe.

With Alexander present, Kirk communicates with the Enterprise and informs Scotty, "I have something unexpected for you. I'm bringing a guest on board."