The complaint in question – as you correctly noted in the body of the post – is in regard to the WASHINGTON Redskins, not CHICAGO.

But you weren’t that far off. Chicago does have a sports club with a Native American connection: the Chicago Blackhawks (Black Hawk was a native chief that was defeated when he invaded Illinois in 1832). CHicagoans are also likely to follow the Fighting Illini of the University of Illinois.