NSRC-North Shore Radio Club
DARC-Dupage Amateur Radio Club
MARC-Metro Amateur Radio Club
BARS-Bolingbrook Amateur Radio Society
WARC-Wilmington Amateur Radio Club
Metro DX Club
WCRA - Wheaton Community Radio Amateurs
York Amateur Radio Club - Elmhurst
Fox River Radio League 
Chicago FM Radio Club 

There are many more clubs in the Chicagoland area. The best way to search for a club near you is to visit The America Relay Radio League website ARRL.org Find a club.  Or you can open this Excel spreadsheet that shows all of the clubs within 50 miles of Chicago