The Federation starship USS Enterprise responds to a distress call from an uncharted planet. A landing party beams down to locate the source and promptly finds a humanoid male and female, Rojan and Kelinda of the Kelvan Empire; they quickly paralyze Kirk and the landing party and orders Kirk to surrender the Enterprise. Rojan tells Kirk that the Kelvans originate from the Andromeda Galaxy and have come to find planets suitable for conquest in the Milky Way galaxy. As their ship was destroyed by a negative-energy barrier at the galactic rim, they needed the Enterprise to make the 300-year return journey home. Three other Kelvans transport aboard the Enterprise and quickly gain control of the ship.

Rojan orders the landing party to a cave guarded by Kelinda. Mr. Spock uses his Vulcan telepathic ability to lure her into the cave, where Kirk knocks her unconscious and seizes her control belt. However, their freedom is short-lived. As punishment, Rojan orders Kelvan Hanar to activate his belt, transforming two landing team members into small blocks of chalk-like cubes. Unfortunately, one of the team members was Yeoman Leslie Thompson, the only "Red Shirt" female, to die on an away mission under the command of Kirk. Rojan picks up the blocks and crushes one to dust, killing Yeoman Thompson. He then transforms the other block (Lt. Shea) into human form.

Back in their cell, Spock relates the experience of his mental contact with Kelinda. The Kelvans, it seems, are not humanoid but have taken human form; they are massive creatures with hundreds of tentacles.

Kirk and Spock try to adapt McCoy's neural scanning equipment into a countermeasure to the Kelvans' paralysis field. Spock feigns illness by placing himself into a deep trance as a pretext for beaming back to the ship. The Kelvans transport the remaining landing party and themselves to the ship shortly afterward.

Spock determines that there is no hope of penetrating the paralysis field projector's casing. So instead, he has Scotty rig the matter/antimatter system to explode on contact with the barrier, ready to use on Kirk's order.

Once the ship has crossed the galactic barrier, the Kelvans change all personnel from the Enterprise, except Kirk, Scotty, Spock, and McCoy, into chalk-like blocks. Spock remembers more from his mental contact with Kelinda and reveals that the Kelvans, in their natural form, have feeble senses and emotions, but in their present form, they have human reactions. So Kirk decides to use their inexperience with feelings against them. The four remaining officers split up, each targeting a Kelvan and introducing them to a different form of sensory overload.

Scott introduces the Kelvan engineer Tomar to alcoholic beverages. Soon Scott and Tomar polish off a bottle of Saurian brandy, leaving both men drunk. McCoy injects Hanar with a "supplement" that is a stimulant causing him to question Tomar's leadership. Over a three-dimensional chess game with Spock, Rojan expresses his confusion about the "apology." Spock suggests Kirk and Kelinda's relationship may be more than captor and captive. Rojan experiences jealousy for the first time. Kirk begins a flirtation with Kelinda, fueling Rojan's jealousy. Kirk gets Rojan to attack him and, in the course of the fight, points out that Rojan is behaving like a human and that his descendants who reach the Andromeda Galaxy will be alien inferiors in the eyes of the Kelvans.

Finally, realizing Kirk is correct, Rojan relinquishes control of the ship to Kirk, who gives the order to return "home" to our galaxy. The world on which Rojan and his people were marooned is suggested as their new home. Rojan considers a life with these new physical sensations and asks Kelinda if she'll stay with him.

Cheers,
Hophead Jon