A landing party from the Enterprise beams aboard Psi 2000, an ancient planet about to break up. They find all six of the crew manning the station dead. The circumstances are bizarre, however, since the life support systems have been switched off and everything in the station is frozen solid. Crewman Joey unwisely removes his gloves is contaminated by a red liquid. When Joey and Spock return to the Enterprise, both are given a clean bill of health (for Spock, this is a pulse of 242 and a practically nonexistent blood pressure). However, Joey notices a strange itch and begins to act irritably and irrationally. He threatens Sulu with a knife, then attempts to turn it on himself. To McCoy's surprise, Joey soon dies from the inconsequential wounds which result. The infection afflicting Joey begin spreading like wildfire, infecting almost all crew members of the Enterprise in very short order.
As Psi 2000 shows a shift in magnetic field (and mass!), the Enterprise begins a close orbit requiring constant vigilance. Meanwhile, Sulu abandons his post for a jaunt at the gym, believing himself to be a rapier-brandishing French cavalier. Riley takes over the engine room and declares himself Captain. He demands ice cream for the entire crew, and begins a ship-wide broadcast of his personal rendition of classic Irish ballads (his favorite being ``Kathleen'').
As the Enterprise begins spiraling downward, Scotty attempts to cut through the bulkhead to regain control from Riley. Scotty displays a stroke of genius, when he is able to change the laws of physics in under an hour saying, "Ya can't change the laws of physics! I've got to have thirty minutes!"
While all this is going on, Nurse Chapel infects Spock and professes to love him. This is extremely difficult for Spock, especially since the infection is causing him to become excessively emotional. Spock then passes the infection on to Kirk, who begins exhibiting paranoia and loss of ability to command. Kirk is reduced to an ineffectual hand-wringer who can do nothing except agonize over the fear that he is losing command of the Enterprise. Luckily, Bones finds the antidote just in time and Riley is dislodged before the audience's ears are permanently damaged by his wrenching ballads.
After mixing matter and antimatter at a colder than recommended temperature according to an untested intermix formula, the Enterprise is thrown into a time warp which causes the chronometer to run backwards. This allows the Enterprise to escape the breakup of the planet, returning it 71 hours into the past and therefore before any of the episode's events took place.