'The Alternative Factor' by Don Ingalls

As the Enterprise orbits a dead world, the crew suddenly experiences a moment of ‘non-existence’. Kirk contacts Starfleet Command and learns that the disturbance was felt across the galaxy; his superiors fear that the incident signals an enemy invasion, and so Kirk is ordered to discover its cause. Beaming down to the planet surface, the captain encounters a man named Lazarus, who tells him that the mysterious effect was caused by his enemy; Lazarus has been chasing his nemesis using a time / space craft, and he now wants the Enterprise's dilithium crystals in order to continue his pursuit. Kirk refuses, and instead takes Lazarus aboard his ship. But there is obviously something very peculiar about the strange man, who suffers from extreme mood swings, and whose head wound continually disappears and then reappears. After Lazarus manages to steal the dilithium he returns to the planet surface; Kirk gives chase, only to discover that Lazarus is in fact two people: one sane and the other a madman, one from this universe, and the other from one comprised of anti-matter. Kirk is confronted by the sane Lazarus, who informs him that should both of them inhabit the same place at the same time, both universes will be utterly destroyed…

William Shatner (Captain James Tiberius Kirk), Leonard Nimoy (First Officer Lieutenant Commander Spock), DeForest Kelley (Doctor Leonard H. ‘Bones’ McCoy), Nichelle Nichols (Lieutenant Nyota Uhura), Robert Brown (Lazarus A and B), Janet MacLachien (Lieutenant Charlene Masters), Richard Derr (Commodore Barstow), Eddie Paskey (Lieutenant Leslie)

Directed by Gerd Oswald

TX:
30th March, 1967

Notes:
*Featuring Captain James Tiberius Kirk, First Officer Lieutenant Commander Spock, Doctor Leonard H. ‘Bones’ McCoy, Lieutenant Nyota Uhura and Lieutenant Leslie