Crowley was born in Vicksburg, Mississippi. After graduating from The Catholic University of America (studying acting and show business) in Washington, D.C. in 1957, Crowley headed west to Hollywood, where he worked for a number of television production companies before meeting Natalie Wood on the set of her film Splendor in the Grass. Wood hired him as her assistant, primarily to give him ample free time to work on his gay-themed play The Boys in the Band, which opened off-Broadway on April 14, 1968 and enjoyed a run of 1,000 performances. Crowley became part of Wood's inner circle of friends that she called "the nucleus", whose main requirement was that they pass a "kindness" test.