When the Enterprise responds to a distress call on the scientific colony on Triacus, Bones, Kirk, and Spock discover that all of the adults to have committed suicide using the drug cylotin. Kirk spots a single survivor, Prof. Starnes, but he does not seem to recognize Kirk and subsequently dies in Kirk's arms. A recording reveals that the colonists felt compelled to destroy themselves to escape what they call ``the enemy within.''
However, the children of the colonists (Tommy Starnes, Don Tsing Tau, Mary, Steve, and Ray; last names Janowski, O'Connel, and Wilkins, not necessarily in that order), appear to be in fine health and pay no attention to the absence of their parents. They are beamed up to the Enterprise, and an examination by McCoy reveals nothing amiss. Kirk tries to question the children and finds that they hated the planet and felt resentful that their parents liked it. Before Kirk can find out anything else, the children begin repeating ``busy, busy, busy,'' and refuse to say anything more. Kirk tries talking to Tommy alone, but he only repeats the behavior of his friends.
When they are left alone, the children perform a summoning ritual for the ``friendly angel.'' The angel gives them instructions for their next ``task,'' which consists of bringing the Enterprise to Marcus 12 instead of Kirk's intended Starbase 4. On Marcus 12, the angel promises that they will find many friends to make them strong, and that this will allow him to take over the universe and allow the children unlimited freedom and play. The children prepare to use strange powers (invoked by up and down motions of a clenched fist) to influence the minds of the crew and take the Enterprise out of orbit and towards Marcus 12.
Clues to events which took place on Triacus are given by a series of recorded messages by Prof. Starnes. These document the onset of paranoia and loss of control over actions immediately following the excavation of a cave by Wilkins. At this juncture, Tommy enters the bridge and uses the opportunity to cause the tape to malfunction before his father's message can be completed. Tommy remains on the bridge after Kirk and Spock leave to consult in private. Tommy influences Sulu to leave orbit, giving him the illusion that the viewing screen shows the Enterprise to still be in orbit. When Uhura notices that the Enterprise is no longer in orbit, she confronts Sulu, but the children soon give her the same illusion as Sulu.
In the engine room, another child causes two engineers to guard the controls and to knock out Scotty when he tries to get them back and put the Enterprise back on course. Spock and Kirk listen to the rest of Dr. Starnes' tape in private, and find that he was being influenced to do things against his will, including requesting a spaceship from Starfleet despite the fact that he had no need for it. Consulting the computer's memory banks, Spock discovers a legend that Triacus was previously inhabited by a band of marauders who terrorized the Epsilon Indi system. The legend also maintains that the marauders, who were eventually wiped out, are waiting to return and maraud again.
Kirk beams down a pair of guards to take over from the security detachment on Triacus, assuming that the Enterprise is still in orbit since he has given no orders for it to do otherwise. When he then attempts to beam up the security detachment, Spock is unable to lock on, and Kirk is forced to face the fact that he has just beamed two men into a vacuum. When Kirk and Spock rush to the bridge, they get a look at the alien influencing the children (who have assembled on the bridge and performed another summoning ritual). Kirk gives commands to Sulu and Uhura to change course and send a message to Starfleet, but the children make Sulu see a passage of knives and Uhura a picture of herself as old and sick, and neither carries out the order. Kirk then orders Spock to send the message to Starfleet, but he is also unable to obey. When Kirk tries to order the security officer to confine Sulu to quarters, the children cause his speech to sound garbled. Kirk then becomes paranoid about losing the Enterprise, but Spock grabs him and the two of them escape from the bridge on the elevator.
They go to auxiliary control and try to enlist Scotty's help in overriding the ship's controls, but Scott and his engineers are firmly under the children's control. Chekov and two security guards attempt to arrest Kirk and Spock at phaser-point, but Kirk and Spock are able to fight their way out of it. Kirk finally manages to free the children of the Gorgon's evil influence and regain control of the Enterprise by replaying the taped ritual and summoning the Gorgon. With the help of tapes of the children playing with their parents, Kirk shows the children the Gorgon's wickedness in killing their parents. When the children cry and desert him, the Gorgon becomes disfigured, then disintegrates, chanting ``death to you all.''