The Enterprise chances across a DY-100 class ship, launched from Earth "in the 1990s". It carries around seventy people, who have been hibernating since their launch. The ship's systems revive the leader, whom Kirk soon learns is Khan Noonien Singh, the leader of a group of genetically enhanced "supermen" who nearly took control of Earth during the Eugenics Wars. They have essentially fled to the future, and with their capabilities, Khan plans to revive his campaign to place "superior" men in positions of leadership.

The Federation established a colony on Omicron Ceti III before it knew that the system's star emitted Berthold Rays, which degrade animal tissue. Tolerable for short periods with precautions, these rays spelled doom for the colony. So how are they still alive, and in better health than when they left Federation space? And perhaps more importantly, why have they accomplished... nothing? The answer threatens the Enterprise...