It's 1958 in Greenwich, Connecticut (USA). Allen Quimp is an English teacher who is getting exasperated by his wife's constant tantrums. He allows himself a little break, by lying to his wife that his real job is spying.
The real CIA intervenes and is very interested by this "agent" who they don't know. He's too popular to get rid of or to risk an incident which makes them look stupid. The CIA send Allen (and his wife) to a quiet place: Cuba.