There is a weapons "restriction" in Chicago. While the 2nd Amendment may imply that it's the right of an American to bear arms, there are legal loop-holes that allows you to essentially ban them.
Take the "restriction" on Marijuana. In order to legally possess marijuana, you need to pay a "ticket tax." Without the ticket tax, any marijuana in your possession is illegal. But here is the catch, in order to obtain the ticket tax, you need to present the drug to some government agency to process it. As a result, you need to be in possession of the drug first, which is illegal since you don't have the ticket tax.
Same concept can be used with firearms. It's not really a ban, but a restriction that makes it impossible to legally posses them.