Brown has been involved with theater since the beginning of her career. She appeared in the 1975 New York Shakespeare Festival production of The Comedy of Errors. Among her earlier roles was a run as Lucy Brown in the 1976 production of The Threepenny Opera, produced by Joe Papp and directed by Richard Foreman. She left the production for film work, but after being away from the production for eight months, Ellen Greene, who was playing the part of Jenny, fell ill. Brown astounded the stage manager of the production by coming in and, with one hour of rehearsal, put on a "brilliant" performance as Jenny. Her first major appearance on Broadway came in 1989, in the play Secret Rapture, written by David Hare.