Mr. Spock is abducted from the bridge of the Starship Enterprise by a mysterious alien woman, and returned to sickbay, without his brain. The operation was done well, with no trauma, but Doctor Leonard McCoy says that his brain must be returned within about 24 hours.
The Enterprise manages to find the ship of the abductor, and persues it to Sigma Draconis 6. They discover the planet's native species has two cultures - males who live on the surface in relative barbarity, and females who live underground. They have stolen Spock's brain to act as a controller for their central computer. McCoy manages to, with aid of the computer itself, hook Spock's brain back up to his body.