Delaney, an Irish American, was born on November 29, 1961, in Philadelphia, Pennsylvania, the daughter of Joan and Jack Delaney. Delaney's mother was a homemaker and her father a union official and former head of the United Auto Workers. She was raised Roman Catholic. Delaney grew up in Roxborough and has four brothers: Ed, John, Keith, and Patrick. While she was attending J. W. Hallahan Catholic Girls High School, she worked as a model for the Elite agency. After her graduation, she went to New York and found employment there as a model. At the same time, she studied acting with william Esper.