Wilbur Wood had bounced around from the majors to minors in two organizations (Boston and Pittsburgh) for a few years, and when he was traded to the Chicago White Sox in 1966 for a Player to be Named Later, nobody really paid attention.

Eddie Cicotte was known to be an inconsistent player when he was with the Boston Red Sox, and he would run afoul of Red Sox management who sold him to Chicago during the 1912 Season. 

In terms of iconic figures, would have been wrong if we placed Minnie Minoso at number one?  Clearly, we didn't, but the native of Havana, Cuba, will always be one of the most revered athletes in the history of Chicago.