The derelict DY100 class spaceship S.S. Botany Bay built in the 1990s is discovered by the Enterprise. Biological scanners detect life aboard, but only 4 heartbeats a minute, so Bones does not believe them to be produced by humans. The Enterprise has no record of the ship, but this is not surprising as many records were lost in the great World War of Eugenics fought during that period.
Bones, Scotty, Kirk and historian Marla McGivers beam aboard and discover it is indeed an old Earth ship powered by primitive nuclear power. The crew is in suspended animation, but the leader is accidentally awakened when the lights are turned on. Kirk is forced to break the glass and remove him from his chamber when the revival procedure fails and he is almost killed. McCoy and the man are then beamed aboard the Enterprise.
As the Enterprise proceeds to Starbase 12 in the Gamma 400 star system, historian McGivers falls in love with the leader (who is discovered to be Khan Noonien Singh). Khan makes a miraculous recovery, and holds Bones at scalpel-point to find out where he is. Khan and his crew are products of the Eugenics Wars of the 1990s. In 1993, a group of supermen simultaneously seized power in more than 40 nations. Spock reveals to Kirk that his research has determined that that there were 80-90 supermen unaccounted for at the end of the war. This, together with Khan's extreme strength and physical prowess lead Kirk and Spock to wonder if there passenger might be one of the missing supermen. Through subtle questioning, Kirk gets Khan to inadvertently admit that he is one of the supermen when he blurts out ``We offered the world order.'' Kirk and company look up Khan in the database and find him to have been the most dangerous of the supermen, and at one time to have ruled a quarter of the Earth.
Khan uses his great strength to break out of his cabin, and McGivers helps him to transport to the Botany Bay. Khan awakens the 72 out of 84 superhumans (30 of them women) whose life support systems are still functioning and takes over the Enterprise with their help. Khan cuts off life support to the bridge, knocking out Kirk, Spock, McCoy, Scott, Uhura, Technicians First Class Tooly and Harrison, and Lt. Spinelli.
When Khan puts Kirk in a decompression chamber to force the other command crew members to join him, McGivers relents and helps Kirk regain control of the ship by cutting off the monitor camera on the chamber, injecting the guard, and releasing Kirk. Kirk then helps Spock escape when he is brought to the chamber for his turn. They gas the entire ship, but Khan escapes to engineering and attempts to cause the ship to self-destruct. Kirk takes on Khan in hand-to-hand combat, and is able to overcome him using a rod which he pulls from the control panel.
Kirk maroons the superhumans on Ceti Alpha 5, leaving them sufficient supplies to enable them to colonize the uninhabited planet. On hearing this, Khan asks Kirk if he has ever read Milton, and Kirk says yes, he understands. The reference is the statement Lucifer made when he fell into the pit, ``It is better to rule in Hell than suffer in Heaven.'' Kirk gives McGivers a choice between court martial and being left behind with Khan, and she elects to stay with Khan.
This episode was the basis for the movie Star Trek II: The Wrath of Khan.