Gregg attended the University of Alberta to work toward a medical degree, and playing hockey was a secondary priority. However, he became one of the top players in Canadian university hockey, leading the Golden Bears to two Canadian Interuniversity Athletics Union (CIAU) championships, and was CIAU Player of the Year in 1979. He received a contract offer from the New York Rangers but rejected it to spend the year with Father David Bauer and the Canadian national team, and captained Canada's entry at the 1980 Winter Olympics in Lake Placid.