Just fifteen times in the modern history of the four major professional sports leagues (NFL, NBA, NHL, MLB) has a team managed to win three or more championships in consecutive order.
New York Greek Americans
The very first Semifinal round of the US Open Cup (then called the National Challenge Cup) saw a pair of Brooklyn teams reach the Final. On April 18, the Brooklyn Field Club, which finished first in the National Association Football League, defeated New Bedford FC 2-1, on two goals by Hall of Famer Robert Millar, after Beckton had given the New Englanders a 1-0 lead. Both teams played much of the game with ten men each, after Clark of Brooklyn and Chadwick of New Bedford were sent off in the 35th minute for fighting.