Olczyk grew up in Niles, Illinois and Palos Heights, Illinois and went to Brother Rice Catholic High School. He was a star on the Illinois midget AAA team (Team Illinois) that won the 1982 national title against a Detroit Compuware squad that featured future NHL stars Pat LaFontaine and Al Iafrate. He then moved to Canada to play for the Stratford Cullitons junior team before joining the 1984 U.S. Olympic hockey team.