The Enterprise investigating a distress signal, and finds a derelict spaceship from Earth’s late 20th century. The ship’s hull is damaged by meteors but Spock determines that its name is the S.S. Botany Bay, but there are no records. The ship appears to have left Earth in the 1990s, during the time of the Eugenics Wars. Kirk takes over a party to investigate, and has Lieutenant Marla McGivers accompany them as the ship’s historian. Beaming aboard, they discover that the passengers are in sleeper cells and one of the chambers begins to revive. McGivers is awestruck by the handsome figure of a man inside, which she identifies as the leader, set to awaken first. The chamber malfunctions and Kirk breaks it open, and McCoy tries to keep the leader alive.
Spock can find no record of the vessel. Kirk suspects that since Botany Bay was an Australian penal colony, this might have been a way to deport criminals. Spock refutes this, having no other explanation of his own. Spock also notes the extremely low probability that a vessel of this type could have survived for so long, and managed to leave Earth’s solar system. Kirk orders the Botany Bay to be put under tow, and to set course to Starbase 12.
In sickbay, Kirk comes to speak to the man. McCoy notes his superior bodily strength and efficiency of his lungs, hinting at his Augment origin.
The man awakens from his slumber and stretches, and notes a scalpel on the wall. He takes it, and moves back to his bed, feigning sleep. McCoy arrives to check his vital signs, and the man reaches towards McCoy’s throat, threatening him with the scalpel. McCoy sarcastically, and in an admirable display of calm, says that if the man wished to kill him, it would be best if he would cut the carotid artery, just under the left ear. The man says he admires such bravery, and lets McCoy take back the scalpel. The man demands to speak to the captain of the vessel, and McCoy calls Kirk, saying he is a man with “many questions.”
Kirk arrives, identifies himself as the captain, and asks the man his name. The man avoids the question, and asks what the ship’s heading is. Kirk answers that it is Starbase 12, a planet in the Gamma 400 star system, the command base in that sector. The man identifies himself simply as “Khan.” Kirk attempts to question Khan further, but he declines to elaborate on his history, acting fatigued. He says that he was once an engineer of sorts, and would like to study the ship’s technical manuals.
Khan seizes control of the Enterprise after coercing McGivers to help him. With McGivers help, Khan beams over his fellow supermen from the Botany Bay and together, they cut off the life support on the bridge until Kirk decides to cooperate.
The bridge crew suffocates to the point of passing out. When they awaken, they are being held at phaserpoint by Khan’s men in the briefing room while Khan holds Captain Kirk captive in Dr. McCoy’s decompression chamber, and the rest of the bridge crew in the briefing room. Khan threatens to kill the captain if Kirk’s crew doesn’t join with him.
McGivers goes to the decompression chamber, knocks out the guard, and frees the captain. He knocks out Spock’s escort, and the first officer pumps anesthesia gas into the ship while Kirk goes after Khan. Khan manages to escape the gas, escape to Engineering, and cut off the ventilation to that section. Kirk arrives and Khan easily disarms him then reveals he’s set the ship’s engines on overload. With time running out, Kirk fights Khan and is initially overwhelmed by the genetically modified superman’s enhanced strength. Kirk manages to grab a tool and knock out Khan and stop the overload just in time.
Later, Kirk calls a hearing and drops the charges against Khan. Instead, he will dump Khan and his people on the uninhabited but inhabitable Ceti Alpha 5, and leave them to carve out whatever civilization they can. In love with Khan, and to avoid court martial, McGivers chooses to go with Khan.
As soon as Khan and his people leave, Kirk and Spock express an interest in returning to Ceti Alpha V in a hundred years to learn what crop will sprout from the seed they planted, unaware of their eventual re-encounter with the genetically superior tyrant fifteen years later.