On arrival at Ekos, the Enterprise is the target of a nuclear missile attack, a technology which didn't exist the last time a Federation ship visited the planet. Kirk and Spock beam down to investigate, discovering that the government on Ekos has been transformed into a Nazi police state which came about when Federation teacher John Gill tried to simply increase the efficiency of the government on Ekos. Gill is now under the control of the people he has tried to educate, and anyone who tries to reveal the truth about Gill or rescue him - including Kirk and Spock - are hunted men.
