Bread and Circuses

The Enterprise follows the wreckage of the S.S. Beagle to a planet where they discover an Earth-like civilization, except that Rome never fell, and rules a world much like twentieth century America. Intercepted radio transmissions suggest deeper mysteries, so Kirk, Spock and McCoy beam down to investigate, and then find themselves caught between the Roman government and a group of "sun worshippers". Proconsul Claudius wants Kirk to beam down his entire crew; the Proconsul is determined that no one will leave this world!