Before the 1926–27 season, the Toronto St. Pats sold Dye to the Chicago Black Hawks, a new NHL franchise. Dye had an outstanding season in Chicago, again leading the league in goals scored on the NHL's highest-scoring team, playing on a line with fellow Hamilton-born player Dick Irvin, who led the league in assists. Unfortunately, both players would soon suffer serious injuries that curtailed their playing careers. At training camp before the next season, Dye's leg was broken and he was never the same player again. He went scoreless for the Black Hawks in 10 games in the 1927–28 season and was then sold to the New York Americans. Over 42 games in 1928–29, Dye had just one goal for the Americans. In November 1929, he was traded to the minor league New Haven Eagles of the Canadian-American Hockey League.