In answer to a distress call, the Federation starship Enterprise arrives at the planet Scalos. Captain Kirk beams down with a landing party to a city with no evidence of life except for an intermittent insect-like buzzing. Crewman Compton disappears before Dr. McCoy's eyes, and Kirk orders the away team back to the Enterprise. Upon their return, the ship begins to experience strange malfunctions, and Engineering reports the sudden appearance of an unknown device attached to the ship's life support systems. Kirk and Spock attempt to disconnect the machine but are prevented by an unseen force.

On the bridge, Kirk decides to allow the unseen enemy to take the next step and asks for coffee. As he sips it, the bridge crew appears to slow down. A woman who kisses him before introducing herself as Deela, "the enemy," appears. She explains that Kirk has been placed in a state of hyper-acceleration, rendering him invisible to the rest of his crew but allowing him to see and hear the Scalosians.

Kirk returns to Life Support and discovers that Compton is still alive, having also been accelerated, and is willingly working with the Scalosians. After confronting Deela's chief scientist Rael, Kirk surmises that the unknown device is intended to turn the Enterprise into a cryogenic storage unit. He records a message to Spock explaining what he has learned; Deela, confidence in her people's success, allows this. Their plan, she explains, is to use the Enterprise crew to help propagate their species, whose men have been rendered sterile by the same natural disaster that caused their accelerated state. After a heated debate on the ethics of this plan, Kirk rushes away and disables the transporter. Deela, finding it inoperative, pretends to believe Kirk's claim to be ignorant of the problem.

Kirk begins to exhibit the acquiescence seen with Compton; however, this ruse allows him to seize Deela's weapon. On his way to Life Support, Kirk meets newly accelerated Spock, who has heard Kirk's message and determined the cause of his hyper-acceleration was a dose of the polluted Scalosian water. The two arrive at Life Support, where Kirk uses the Scalosian weapon to stun Rael and destroy the cryogenic device. After transporting Deela and her party back to the planet, Spock reveals that he has brought a possible antidote to the Scalosian water. Kirk takes a dose immediately, while Spock takes advantage of his accelerated state to effect repairs on the Enterprise.