The Enterprise arrives at the Zeta Centauri system, seeking class "M" planets for study. Uhura receives an emergency transmission from the planet Argylus 13, but she is unable to make contact with the source. Reviewing the ship's records, Kirk and Spock discover that the planet has an atmosphere comparable to Earth, and is rated 17 on the industrial scale - indicating a highly advanced civilization. The two beam down to the planet to investigate, along with Mr. Scott, Mr. Sulu and Nurse Chapel.
The landing party is brought inside the castle, before a young, blonde headed young man sitting on a throne. "Welcome, men of the Enterprise!" he says. "You know who we are!" exclaims Kirk. "Then it was you who sent the distress signal?" "Not personally" the young man replies, "but it was done at my command. I am called Simon, and I am the ruler here! Now I suppose you're wondering why you were led here. I shall attempt to explain. Argylus is a very advanced civilization. In fact, the children of Argylus have fully matured intellects at the age of three! But seven years ago, Argylus was stricken by a great plague which killed all the elders; an unknown virus struck all over the age of thirteen!"
On board the Enterprise, Dr. McCoy researches the virus symptoms, and locates an antidote. It is a rare herb called "Genitum Lars", that the ship does not carry on board. He runs a search through the computer, and discovers that the nearest planet with Genitum Lars is Ominnus, but the planet is located on the other end of the galaxy! He radios the news to the Captain and the rest of the landing party, telling them that Ominnus is a two-day journey each way. "If anything should delay you, Doctor, you're going to lose a captain, a chief engineer, and a good nurse!" Kirk says. He orders Spock to take the Enterprise to Ominnus at high speed to get the antidote. Meanwhile, the landing party visits the medical research facility on the planet.
Meanwhile aboard the Enterprise, Spock orders the ship to increase speed to warp 8. McCoy warns him that at that speed, the field mechanism may not be able to compensate for the strain. "We'll have to risk it Doctor" Spock answers. "The lives of the Captain and three crewmen are at stake!" Just then, a large meteor appears on a collision course with the ship! Spock explains that at such extremely high speed, the power of the deflectors is weakened, and cannot ward the object off course. He quickly orders the ship to warp 6, slowing it directly in the path of the asteroid! His tactic pays off, and the asteroid is diverted by the deflector screens. The ship continues on toward Ominnus.
On Argylus, the landing party is experimenting with possible remedies in the castle, when a group of boys wearing hooded robes bursts into the room. "So!" the leader says, "Our messengers were right! King Simon has captured a group of outlanders! Bind them securely, squires! King Simon would keep the cure for his own tribe, but Warlord Yago will see that you all benefit from it!" The landing party is taken prisoner and led away across a desert, along with Simon, who has been captured as well. When they arrive at the palace of the Warlord Yago, they are thrown in the castle dungeon. "I don't understand why we were abducted in the first place!" Kirk exclaims after their captors have departed. "When the adults died, the surviving children split into two camps, each with a separate ruler" Simon explains. "There were ideological differences between the two tribes and relations were strained, but until now, Yago and I had always been able to resolve our differences peacefully!" At that moment, a guard informs them through the cell bars that unless they deliver an antidote to Yago within three days, they will be executed!
When the Enterprise arrives at Ominnus, Spock and McCoy beam down to the surface to get the Genitum Lars herb. They are collecting the small plants (which look quite like radishes) when a group of club-carrying cavemen come upon them. "The ugly ones steal from the sacred garden!" shouts the leader, and orders the others to attack. "What are we going to do?" asks McCoy. "The Federation forbids us to interfere with the natural development of a civilization, so we can't use modern weapons against them!" Spock solves the dilemma by taking a nearby stick of wood, and using it to soundly thrash the attacking cavemen, without injuring them. The remaining natives run away in fear. The two men gather the herbs, and then the Enterprise returns to Argylus.
On the planet surface, the landing party passes the time in their cell. Christine tells the others of a verse she read many years ago that went: "Backward, turn backward, o time in your flight. Make me a child again just for tonight!" Then a group of child guards arrives to take the them to their execution. Kirk orders the others to make a break for it, and they grab the childrens' weapons. Another group of children led by Yago appears, carrying guns. Kirk is forced to shoot them before they fire at him. They aren't even wounded! Kirk is shocked. "Why not?" says Yago, "These rifles fire only harmless rays of light! It was merely a game; an elaborate charade set up for my own amusement. Simon believes that a cure for our disease may be found! I harbor no such hopes. I know that we are all merely waiting to die, so I create these little games to make the waiting more bearable!" The landing party realizes that they are not prisoners after all!
As the ship leaves orbit, Kirk makes an entry in his personal log: "Star date 18:32.9. Our mission on Argylus complete, we have set out for points undetermined, yet my thoughts are back with the children. Their civilization shows promise and I suspect that soon the child shall truly be father to the man!"