No. Any place that does licenses can do it. As long as there's a notary somewhere to notarize it. I've done it at a gun show. I've done it at "Mary's Fast License Service". Gunshops will often have the forms, as will police stations, etc.
(oop. sorry. I misread you to mean that it had to go through a gunshop.)
Actually, the Illinois State Police has the application on their website. You can print it up, get a picture, write a check for $5 and mail it in all by yourself. No notary required.
Here's the link:
http://www.isp.state.il.us/media/docdetails.cfm?DocID=38