Kennedy was born Adrienne Hawkins on September 13, 1931, in Pittsburgh, Pennsylvania. She was raised in an ethnically diverse neighborhood in Cleveland, Ohio, where her father worked as a social worker and her mother was a schoolteacher.

When Kennedy entered Ohio State University in 1949, she experienced racism for the first time. Upon graduation in 1953, with a B.A. in education, Kennedy married Joseph C. Kennedy; the couple had two sons together before their divorce in 1966.

Kennedy began writing plays as early as the mid-1950s. When her husband returned from serving in the Korean War, the couple moved to New York City. She began her graduate studies in creative writing at various institutions and some of her fiction was published in the early 1960s.

To gain entrance into playwright Edward Albee' s workshop at Circle in the Square Theatre, Kennedy submitted two of her plays. One was called...