The title of the film, set in Luxembourg in 1942, during the Nazi occupation, amalgamates the words Schacko (helmet) and chapeau claque (opera hat). The village, in which it is set, has not yet been feeling the effects of the war at this point.

After his wife dies, middle-aged businessman Philip Emmenthal, at the prompting of his playboy son Storey, populates his Geneva villa with eight-and-a-half concubines. Three are from Kyoto, where Storey manages Pachinco palaces. Each has a distinctive personality: a nun, a child bearer, a gambler, a student of Kabuki, a horsewoman with a pet pig, a maid. As a year passes, the women begin asserting their own power.

Luxembourg, October 1830. Unrest spreads in the region in the wake of the Belgian Revolution. Fed up with the domination of the Dutch, most of the people want to become Belgian. Those who want an independent Luxembourg are few. Among them a town clerk obstinately refuses to accept the Belgian nationality. Considered as a traitor, he is forced to go into exile. A few years later, in 1839, Luxembourg finally becomes independent.

Ofelia is the daughter of photographer Miguel and of deceased circus artist Lea. When her father is hospitalised with a nervous breakdown, she decides to find out the reason and in doing so discovers the truth about the relationship between her parents and the true fate of her mother.