It has been a very long time since there were any gun shops in Chicago. The only ones I remember were HH Harris & Klein's & they could only sell a handgun to a Chicago resident with a permit issued by the PD. Harris was located next to the PD's Headquarters, 11th & State. The owner, Herb was married to either Smith or Wesson's grand daughter & had S&W's that no one else could obtain.
The only other shops in the city that I recall were Abercrombie & Fitch when they sold high end rifles & shotguns & the old Marshal Fields. They had a gunsmith in their men's annex back in the early 70's.