While in orbit around a planet rich in the high-energy mineral kironide the Enterprise receives a distress call from the surface. Kirk, McCoy and Spock beam down where they are greeted by a dwarf dressed in clothing similar to that worn by the Ancient Greeks who introduces himself as Alexander. He takes them to meet his people who call themselves Platonians in honour of the Greek philosopher Plato as they spent some time on the planet Earth during the Greek golden age and now style their culture along the same lines.

A woman called Philana asks them to examine her husband's infected leg. McCoy goes to take a look at the man but before he can get close to his patient, named Parmen, a hypospray flies out of his medical bag, towards the man, all by itself. Parmen is delirious with a fever caused by the leg infection and his telekinetic abilities cause strange things to happen until he is sedated. After McCoy's treatment he recovers from the fever and asks that the doctor be allowed to stay with them. Kirk naturally refuses the request upon which he and Spock are subjected to psychokinetic torture.

The Platonians' powers are due to their consumption of the planet's food and water which has a high content of kironide in it. The dwarf, Alexander, does not possess their telekinetic ability as his digestive system is unable to absorb the kironide and is unable to defend himself as he is bullied and mistreated by the others. McCoy secretly injects Kirk and Spock with a powerful concentrate of kironide.

Parmen, requiring entertainment, forces Nurse Christine Chapel and Lieutenant Uhura to beam down from the ship and, together with Kirk and Spock, perform for him. The Enterprise personnel have been kind to Alexander and he doesn't like seeing his newly found friends treated in this way. He attacks Parmen with a knife but is stopped in his tracks by Parmen's telekinetic powers and has the weapon slowly turned on himself. In the time that has passed since McCoy's injection the kironide concentrate has started to take effect on Kirk who explores his new powers by mentally wrestling with Parmen for control of the knife.

Kirk's will proves to be the stronger and the knife is slowly forced away from Alexander and towards Parmen's throat. The Platonian admits defeat and begs for mercy, being forced to promise to mend his bullying ways. Kirk warns him that the events will be reported to Starfleet and, if he goes back on his word, the powers can be recreated whenever they wish in order to punish him. The Enterprise crew leaves the Platonians and beams back to the Enterprise, taking Alexander with them. He has no wish to remain with his tormentors or to acquire powers like theirs even though McCoy would be able to arrange it for him.