The Alternative Factor
S01E27 - Airdate: 1967-03-30
Runtime: 60 min
An alien named Lazarus is somehow responsible for a kind of "winking out" effect - all of reality seems on the verge of collapse. He is fleeing a monster whose intent is nothing less than the destruction of reality. But through a mishap, Kirk is transported to the home of that monster. And he looks exactly like Lazarus! Kirk must decide which of them - if either - is the monster. If he guesses wrong, it's the end of everything.
Episode details and rating from TVmaze.