The Chicago native was a star on the Illinois Midget team that won a national title when it upset the Detroit Compuware squad that featured Al Iafrate and Pat Lafontaine. His next stop was the Stratford Cullitons of the OJBHL where the young talent began to make a name for himself in Canada. Olczyk joined the U.S. national team in 1983 and scored 68 points in 62 exhibition matches. He was one of the top players on the U.S. squad at the 1984 Sarajevo Olympics.

The Chicago Blackhawks traded up at the 1984 NHL Entry Draft to choose their native son third overall. He scored 20 goals as a rookie playing with Troy Murray and Curt Fraser and became a crowd favourite. He scored 79 points in his second year while playing in a number of different situations. In the mid 1980s the young forward was a regular on Team USA at the World Championships, playing at the 1985, 1986, 1987, and 1989 tournaments and suiting up for the Americans at the 1987 Canada Cup.

Prior to the 1987-88 season, Olczyk was traded to the Toronto Maple Leafs along with Al Secord for Rick Vaive and Steve Thomas. Olczyk was an offensive force for the mediocre Leafs. He scored 42 goals that first year then helped Toronto reach .500 in 1980-90 by forming the explosive line with Mark Osborne and Gary Leeman. When the team stumbled the next season, Olczyk and Osborne were sent to the Winnipeg Jets for Dave Ellett and Paul Fenton. He scored well for Winnipeg and helped the U.S. reach the finals of the 1991 Canada Cup.

Olczyk next joined the New York Rangers and was an important team leader in the dressing room and off the ice. Olczyk was also on hand to witness the team's first Stanley Cup in 54 years in 1994. He returned to Winnipeg and scored 27 goals during the franchise's Canadian swan song in 1995-96. Olczyk joined the Pittsburgh Penguins for two seasons before returning to the Blackhawk organization in 1998-99. The hometown native played his final two years in Chicago before closing out his career following the 1999-2000 season.