Young was born on January 25, 1945, in Washington, D.C. She added the surname Taylor, which was the surname of her stepfather, a Detroit executive. Her father was a diplomat, and her younger siblings are actress/sculptor Dey Young and writer/director/producer Lance Young. The siblings were raised in Oakland County, Michigan. Leigh graduated from Groves High School, Beverly Hills, Michigan in 1962. Before attending Northwestern University as an economics major, she spent a summer shifting scenery, modelling, acting, and sweeping up at a Detroit little theater. However, she left Northwestern before graduating to pursue a full-time acting career, making her professional debut on Broadway in Three Bags Full. About dropping out of college, the Actress explained:

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