Stardate 5784.3. The Enterprise diverts to an unknown planet rich in the high-energy source of kironide, in response to a distress signal. Kirk, Spock, and McCoy beam down and are confronted by Alexander, a dwarf and the entertainer to the court. He introduces himself and the others as Platonians, and is then pulled away to the court where their philosopher-king, Parmen is ailing. His wife Philana brings them in and when McCoy tries to give Parmen an injection, Parmen telekinetically injects himself with it. McCoy confirms that Parmen scratched his leg and got a massive infection.
Parmen's condition worsens and McCoy notes that the Platonians have reduced physical resistance. Philana explains they have had telekinesis ever since they arrived on the planet and they have no doctors since they were genetically bred for longevity. She explains that she is 2,300 years old. Parmen goes into delirium and everything in the room moves about randomly. In orbit, the Enterprise is shaken by Parmen's brain waves. Parmen lashes out and he throws back McCoy, then attacks Alexander. Kirk tries to hold him off and McCoy and Philana manage to break Parmen's concentration just in time. Philana asks them to stay and McCoy agrees so he can monitor Parmen.
Alexander is grateful t Kirk for coming to his defense and wants to know if where they come from, no one has the power. Kirk assures him size makes no difference and no one has the power. Alexander is telekinetically pulled out and Spock cautions that the Platonians may not let them leave and give away their secret.
Alexander is performing for a recovered Parmen when Kirk comes in to ask for his ship to be released. Parmen is angered and first disarms Kirk, then forces him to slap himself repeatedly.
Later, Kirk, Spock, and McCoy are telekinetically forced into Parmen's presence where he and Philana offer them gifts in return for their service. Parmen then apologizes for assaulting Kirk and agrees to release the Enterprise… but asks McCoy to arrive. McCoy refuses and tries to leave but Parmen holds him there. Kirk refuses to leave without McCoy and Parmen forces them to stay for their anniversary celebrations. Parmen forces Kirk and Spock to don laurel leaves and dance, then forces Kirk to humble himself. When McCoy still refuses, Parmen has Spock dance a flamenco inches from Kirk's head, then force laughter and then tears from him. They then force Kirk to act like a horse and Alexander renounces him so Parmen forces him to ride Kirk.
Parmen sends them back to their quarters where Spock is meditating on his loss of emotion. Spock admits he has to master his emotions and McCoy says he should stay but Kirk notes that Parmen will kill them once they leave. Alexander confirms Kirk's suspicions and realizes that it wasn't the fact it was inferior. He breaks an urn and plans to stab the Platonians, but Kirk convinces him not to. Alexander explains that the Platonians gained their powers a few months after arriving not he planet, and after they ate the native foods. Spock figures there is a connection and McCoy compares Alexander's blood to Parmen's. He determines that Parmen has kironide broken down through the pituitary gland, and since the gland also regulates bodily growth, Alexander's deficient gland prevents him from gaining power. Spock notes that anyone on the planet long enough would gain the same power. They figure that the Platonians can't combine their powers against them and Alexander confirms they each have a separate power frequency. McCoy distills the kironide and gives Spock and Kirk double the amount Parmen has. Alexander refuses to get an injection, not wanting to be corrupted by the power. He asks them to take him with them. However, they're interrupted when Uhura and Chapel are beamed down and then marched off against their will.
All four of them are forced to don Roman garb and brought before McCoy, Alexander, and the gathered Platonians. Kirk and Spock can't yet access the kironide-based powers. Parmen gives a speech about their anniversary and how they have formed the perfect utopia. He forces Spock to serenade Uhura and Chapel, then forces Spock to kiss Chapel and Kirk to kiss Uhura. Bored, Philana summons instruments of torture and forces Kirk and Spock to go after the female officers. Disgusted, Alexander tries to stab Parmen who stops him and forces him to stab himself. However, Kirk telekinetically takes control of Alexander and announces they can defend themselves. Parmen challenges Kirk and they use Alexander as a weapon, with Kirk proving triumphant.
Alexander denounces Parmen, who quickly backs down. Kirk explains there'll be other starships and Parmen rapidly backsteps. Kirk and Spock don't believe him and warn that they can quickly recreate the telekinesis in hours, and Parmen notes that none of them can be trusted. Kirk is skeptical but prepares to leave… taking Alexander with them.