A long-lived people with telekinetic powers who once lived on Earth in the age of ancient Greece and later forced the Enterprise crew to perform for them.
The Platonians claim to have visited Earth in the time of ancient Greece and modelled their society on Plato's ideals after their own sun went nova. They settled on a remote planet, where traces of kironide in their food gave them powerful psychokinetic abilities and very long lives.
In the episode Plato's Stepchildren, their leader Parmen needed medical care, and Leonard McCoy treated him. The Platonians then wanted McCoy to stay forever and used their powers to humiliate James T. Kirk, Spock, Nyota Uhura and Christine Chapel. McCoy discovered the source of their abilities, gave Kirk and Spock kironide injections, and the crew overcame Parmen with help from Alexander, a Platonian born without powers.