Kirk is a Dinuvian Slime Devil
As is no great surprise, the 3rd last entry in the countdown is "The Trouble with Tribbles" (Polygeminus grex), a species that is born pregnant. With sufficient food a single tribble can quickly increase its number exponentially through presumably asexual reproduction, bearing an average litter of ten every twelve hours.
They next showed up in the DS9 episode, Trials and Tribble-ations Odo mocks Worf upon hearing of the Klingons' slaughter of the tribbles with, "Another glorious chapter in Klingon history. Tell me, do they still sing songs of the Great Tribble Hunt?"
I suspect that the #1 Episode will be "The City on the Edge of Forever", but #2 will be tougher. Personally, I'd like "Gamesters of Triskelion", but I suspect the Japanese viewers would like "The Naked Time" because it features Sulu prominently.
By the way if you wish to adopt a tribble, head on over to this link, tribbles.