After beaming down to investigate a research post whose team had apparently gone mad and killed themselves, members of the landing party bring back a virus that has intoxicating side effects. As the virus spreads through the ship and crew members start acting strangely, Kirk finds himself with a crisis on hand when Lt. Riley (Bruce Hyde) locks himself in the engine room and shuts down the engines ... causing the Enterprise to spiral down out of planetary orbit.
A lot of the sophomoric silliness involving the ship's officers in "drunk mode" is goofy and didn't do much for me. But the real core of "The Naked Time" emerges in its analysis of Spock; when he becomes affected we see just how torn he is between his human emotions and his Vulcan sense of reason and control. Leonard Nimoy's rendition of the role is exceptional. Also of interest is Nurse Chapel's confession of buried feelings for Spock, as well as Kirk's discussion about being essentially married to the ship.
The ending, involving a sci-fi tech procedure that results in time moving backwards, is a non sequitur that's tough to swallow. But at least it shows the writers were trying something imaginative.