Allen was born on October 5, 1951, in Carrollton, Illinois, to Ruth Patricia (née Howell) (1927–2020), a university professor, and Carroll Thompson Allen (1925–2015), an FBI agent. She is of English, Irish, Scottish, and Welsh descent. Her father's job forced the family to move often. "I grew up moving almost every year and so I was always the new kid in school and always, in a way, was deprived of ever really having any lasting friendships", Allen said in 1987. Although Allen says her father was very much involved in the family, she felt that she and her two sisters grew up in a very female-dominated household.
After she graduated from DuVal High School, in Lanham, Maryland, at 17, she moved to New York City to study art and design at Fashion Institute of Technology for two years. Allen later ran a boutique on the University of Maryland campus and spent time traveling through South and Central Asia. She attended George Washington University and began to study and perform with the experimental company, the Washington Theatre Laboratory, in Washington, D.C. In 1974, Allen joined Shakespeare & Company in Massachusetts. Three years later, she moved back to New York City and studied at the Lee Strasberg Theater Institute.
