A titanic force of energy in the form of a luminous green palm materializes and fastens onto the USS Enterprise, preventing it from advancing. Captain James T. Kirk endeavors to break free of the ship, but he is unsuccessful. A human-like vision appears on the bridge's viewscreen and communicates with the crew. Kirk implores that the vessel is released, yet the entity responds by intensifying its grip, warning that it will destroy the ship unless Kirk accedes to its request to transfer the crew to the planet below.

Captain Kirk and a group of officers, one of whom is Lieutenant Carolyn Palamas, who knows Greek mythology, travel to what looks like a classical Greek temple. There, they meet a humanoid who says he is the god, Apollo. He informs the team that he will not permit them to leave and nullifies the communicators and transporter. He demands that the crew of the Enterprise show him reverence as their ancestors did and promise to give them all they desire in return. However, Kirk denies his request.

As Apollo focuses his attention on Carolyn, it greatly offends Mr. Scott, who steps up to protect her from Apollo's approaches. Apollo smashes his phaser and declares he will take Carolyn as his mate. After showing off his strength, Apollo looks exhausted and then vanishes with Carolyn.

Kirk and McCoy hypothesize that the individual who had captured them was one of a bunch of mighty extraterrestrials that had visited Earth thousands of years ago and were revered by the ancient Greeks. However, Chekov noticed Apollo's weariness, so Kirk baited Apollo to assess the magnitude of his strength and let the away team gain the advantage. Meanwhile, Carolyn understood that Apollo was part of a group of sojourners that survived on love and adoration. He is the last survivor of his kind, the others having passed away over the ages.

Kirk's attempt to irritate Apollo is unsuccessful when Carolyn steps in to safeguard the landing crew. Apollo directs Kirk to start the procedure for the rest of the crew to come down to the planet. He takes Carolyn by herself and tells her that she must deny Apollo if they are to be saved from servitude. She reluctantly consents.

At the same time, Mr. Spock could trace the source of the power that created the shield that was trapping the Enterprise and found a way to send and receive transmissions and fire their phasers through it. Unfortunately, Carolyn put her duties as a Starfleet officer first. She told Apollo that her fascination with him was only for scientific purposes, comparing him to a new type of bacteria. This upset Apollo, and he created thunder and lightning in response, prompting Captain Kirk to command Spock to aim for and eradicate the power source.

Apollo spoke to the other gods after his defeat, allowing that he was wrong and asking to be welcomed by them. But, in the end, he disappeared. Carolyn was grief-stricken. Kirk mentioned that humans derived their concept of morality from the Greeks, their culture, and mythology, and, accompanied by McCoy, felt sorry for having had to annihilate Apollo.