Schiff was born in Framingham, Massachusetts to Edward and Sherrill Ann (Glovsky) Schiff. His father was in the "rag business," selling different lines of clothing across the country, which caused the family to move first to Scottsdale, Arizona and then Alamo, California.

Schiff graduated from Danville's Monte Vista High School in the Bay Area, and went on to both Stanford University and Harvard Law School.

After Schiff graduated from Harvard, he moved to Los Angeles to serve as a law clerk for Judge William Matthew Byrne, Jr. Schiff then joined the U.S. Attorney's Office in Los Angeles as a federal prosecutor, where he served for almost six years, most notably prosecuting, Richard Miller, the first FBI agent ever to be indicted for spying for Russia.