Born in Columbia. South Carolina, Chambers began her early writing career by producung scripts for local radio stations. In 1954 she enrolled at Rollins College in Winter Park, Florida, intent on becoming a playwright. after a frustrating period there, she moved to study acting at California's Pasadena Playhouse in 1956.

After one season there, she moved on to New York, then to Poland Spring, Maine, and then back to New York. As she wantd to complete her undergraduate degree, she then enrolled at Goddard College, Vermont, where she met her lover, manager, and life-long companion Beth Allen.

Chambers completed her degree in 1971, receiving the Rosenthal Award for Poetry and a Connecticut Educational Television Award. In 1972 she was given a Eugene O'Neil Fellowship. In 1980 she began working with the Glines, a New York theatre company that focused on plays about lesbians and gays.

In 1981, Chanbers was diagnosed as suffering from cancer. In 1982 she received the Fund for Human Rights Award. After her death, her partner published a collection of her poetry. As one of the first US playwrights to create positive images of lesbians, Chambers is an important figure in gay and lesbian cultural history.