Voyager picks up an automated message from the Kohl settlement, whose members survived an environmental catastrophe by going into artificial hibernation. The crew beams their hibernation pods on board and finds two humanoids dead and three in deep stasis, their minds connected to a sensory system controlled by a computer. The Doctor reveals that the two victims died from heart failure, brought on by mental stress — or extreme fear.

Hoping to learn how to revive the survivors, Kim and Torres enter two pods and are attached to the computer, which allows them to enter the colonists' dream state. They're thrown into an environment that resembles a bizarre carnival run by a malevolent Clown, whose followers quickly drag Kim to a guillotine.

Although the Clown spares Kim, the pair suddenly understand how the Kohl could literally be frightened to death. Because the Clown's survival depends on the colonists' minds remaining linked to the sensory system, the Kohl — and now Kim and Torres — can't awaken because the Clown won't allow it. The computer has manifested the worst fears of their subconscious minds into the persona of the Clown; they are now prisoners to that fear.

The Clown allows Torres to leave so she can warn the Captain that if the hibernation pods are deactivated, everyone will die. While Janeway contemplates how to negotiate, the Clown torments Kim mercilessly. The Doctor is sent to discuss the release of the hostages but the Clown refuses to cooperate, so Janeway decides to mount a rescue mission to free Kim and the Kohl settlers.

Her first plan fails when the Clown catches on to Torres' attempts to disable his program. Infuriated, he puts a colonist in the guillotine, where the frightened man succumbs to heart failure. To prevent more deaths, Janeway orders Torres to stop.

The Captain comes up with a final offer for the Clown: trade the current captives for Janeway herself. The Clown agrees, only to discover that his prize is only a holographic image. With no one alive left to torment, "Fear" is conquered and he disappears forever.