English tailor Leonard (Mark Rylance) creates custom suits on the world-famous Savile Row in London. After suffering a personal tragedy, Leonard relocates to Chicago, where he finds a small tailor shop in a shady neighborhood and buys it, in order to pursue his profession.
The neighborhood is teeming with wealthy families of ruthless gangsters who become his customers. His rapidly becomes well-known in the area. One night, a group of mobsters come knocking at his workshop door in search of a suspicious package and attaché case. As the night progresses, he's lured into the chaos. Everyone wants to claim the prize, which it turns the night into a disastrous bloody dispute. In order to survive, Leonard must outwit the mobsters.