When the Enterprise approaches the inner planet Ecos to investigate the cessation of communication with researcher John Gill, it is attacked with a rocket carrying a nuclear weapon. This is puzzling as well as dangerous, since neither the outer planet Zeon nor the inner planet Ecos is technologically advanced enough to possess rockets or nuclear warheads. The Enterprise retreats to maximum orbital distance and Kirk and Spock beam down (after having position-broadcasting transponders surgically implanted in case of mishaps).
Kirk and Spock discover that a Nazi movement has swept the planet, complete with genocide of the ``Zeon pigs'' residing on Ecos. They view a public newscast in which the Iron Cross second class is presented to Daras, hero of the Fatherland. Kirk and Spock are also shocked to learn that Gill appears to be the leader of the planet's Nazi movement.
When they are approached and questioned by a Nazi Lieutenant, they overpower him and Spock steals his uniform. Spock then pretends that Kirk is a Zeon he has captured and nerve pinches a Gestapo commander who wishes to take charge of Kirk. This provides Kirk's uniform, and Spock compliments Kirk by telling him ``You should make a very convincing Nazi.''
As Kirk and Spock make their way to see the Führer, they are confronted by a Nazi S.S. Major after Spock neglects to salute him. The Major becomes suspicious, and Spock is exposed when he is forced to remove his helmet. Spock and Kirk are then whipped in the process of being interrogated. Nazi Party Chairman Eneg interrupts the ``questioning'' and tells the Nazis to lock up Kirk and Spock for an hour (in contradiction to standing orders to execute prisoners after interrogation).
In prison, Kirk and Spock speak to an imprisoned Zeon (whom they had previously encountered being beaten on the street by the Nazis) and find that the Nazi movement began several years ago (corresponding with the arrival of Gill). They escape from prison by making a primitive laser from the rubindium crystals in their transponders using their cell's incandescent bulb as the excitation source (not quite a flash arc and ruby crystal, but close enough in a pinch). Spock hides outside the cell and then nerve pinches the guard when Kirk summons him under the pretext of wanting to talk. Kirk and Spock also allow the Zeon prisoner to tag along.
Kirk and Spock penetrate Nazi headquarters with the help of Secretary Daras and Chairman Eneg. They discover that Gill is only the drugged puppet of deputy Führer Melakon after he gives a stilted speech unleashing the final assault on Zeon. McCoy is beamed down and manages to barely overcome the drug. Gill tells them that he started the Nazi movement to unify the planet (because it was the ``most efficient system Earth ever knew''). With an extra hypo from Kirk, Gill manages to call back the invasion fleet and denounce Melakon as a traitor. Melakon grabs a machine-gun and kills Gill, only to be shot himself. Chairman Eneg takes over and stops the killing, declaring that ``it is time to live the way our Fürher intended. Kirk and company then return to the Enterprise in peace.