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Bobby Hull and Stan Mikita won the Cup for Chicago in 1961
After the death of the Black Hawks owner Fredric McLaughlin in 1944, ownership passed to Bill Tobin, who was believed to have been a puppet to the Red Wings owner James E. Norris, as discussed here.
Until the late 1950s, Chicago was largely ignored and served to bolster the Red Wings team.
During this period the Black Hawks would miss the playoffs 11 times out of 12 seasons. By the 1958-59 season, Chicago was under new management and would make its first appearance in the finals in five years.
They would lose to the Canadiens twice, once in 1958-59 and again in 1959-60 before their third consecutive playoffs trip, where they met Montreal once more. After having been swept in the series the year before, expectations were low for the Black Hawks.
They would, however, win the Cup for the 1960-61 season, defeating the Canadiens 4-2 in the semifinals and the Red Wings 4-2 in the final series.
The Black Hawks would remain a fixture in the postseason for the next 29 seasons, during which time they would change their name into the standardized one-word version it is today.
Going from an afterthought of Bill Tobin to Stanley Cup champions, added to the nearly three decades of postseason appearances since, the Black Hawks earned the third place on this list.