Ullman's adaptation of the Swedish writer August Strindberg's play will be the most recent version since Mike Figgis' 1999 film.
The story follows a woman as she attempts to escape the stodginess of social mores at a Swedish count's estate in the summer of 1874. Reveling at a servants' dance, she falls for a senior member of the house staff.
Farrell will play the servant suitor.
The role marks Chastain's first film project since her best actress Oscar nomination and Golden Globe win for the Kathryn Bigelow-directed "Zero Dark Thirty."
Oliver Dungey and Teun Hilte are producing.