Although Chelios was born in Chicago, a relatively good place for a boy to learn hockey, his family moved to San Diego in 1977. There were few good players for Chelios to compete with and learn from in southern California. He played in a weekly game with a team of Marines for a while, but even this was not enough. During his senior year of high school, Chelios took a bus to Hawkesbury, Ontario to try out for a junior B league team there. He was cut from the Hawkesbury team after one game, so he tried out for another junior B league team, this one in Chatham, Ontario. That didn't work out either, and Chelios found himself in a bus station in Michigan without enough money to make it home. He borrowed the money, returned to California, and began attending the U.S. International University in San Diego, which had inaugurated a hockey program one year earlier. Chelios did not make the team. Finally, he found a place with a junior B team in Moose Jaw, Saskatchewan.
Chelios's career started looking up in 1981, when he was recruited to play for the University of Wisconsin. Chelios, formerly a forward, credited his time spent playing under famed Wisconsin coach "Badger" Bob Johnson, one of the most successful hockey coaches of all time, with teaching him how to be a solid defensive player. Chelios was drafted by the Montreal Canadiens in 1981, but he remained in college, helping Wisconsin to win the National College Athletic Association (NCAA) hockey championships in 1981 and 1983. Then, after playing with the United States hockey team at the 1984 Olympics, Chelios finally began playing for the Canadiens.