I was under a different impression.
This depends on which bunch of 'Chicago criminals and gangsters' that you're talking about...
The FOID was never intended to stop mobsters from having guns
It was intended to PROTECT mobsters from getting shot by the people they might try to rob/extort/etc
Look at the cities with the heaviest gun control: New York and Chicago. Is it any coincidence that these towns have had long histories with organized crime?
(And lets not forget the organized criminals in DC...)