Eric Daze was drafted 90th overall in the 1993 NHL Entry Draft by the Chicago Blackhawks. Despite his strong junior career, most scouts did not hold him in high regard, questioning both his skating ability and his ruggedness. Daze first rose to prominence while playing Midget hockey with the Laval Regents of the Quebec AAA Midget Hockey League. In 1992-93, he joined the QMJHL's Hull Olympiques, scoring 32 points in 55 games before moving on to the Beauport Harfangs late in the season. The following year with Beauport, he vastly improved on those stats, to 59 goals and 107 points and was named a QMJHL First Team All-Star. In 1994-95, he scored 54 goals and 99 points and was again named a QMJHL First Team All-Star. He won the CHL's Most Sportsmanlike Player award as well as the Viscount Alexander Award, which goes to the Junior Male Athlete of the Year in the province of Quebec.


Daze led the Quebec provincial under-17 Midget team to a silver medal at the 1992 World Hockey Challenge and was a key contributor to the Canadian under-20 junior team that skated to a gold medal at the 1995 World Junior Championships. That year, he was named a tournament All-Star. In a shortened 1994-95 season, the 19-year-old Daze made his NHL debut on April 27 against the Dallas Stars. Just three nights later, he scored his first NHL goal against the Detroit Red Wings. In 1995-96, Daze joined the Blackhawks full-time and collected 30 goals. After a couple of seasons tempered by injuries, Daze returned to form in 2000-01, scoring 33 goals before establishing a career high 38 in 2001-02. Injuries would plague Daze once again in 2002-03, limiting his season to under 60 games for the first time in his nine year career and in 2003-04 suited up for a mere 19 games, while recovering from a back injury. Aside from his World Junior experience, Daze represented Canada at the World Championships (1998-1999).