REBEL,
First, AR15 is a generic name. You can have legal to own semi-auto civilian models of AR15 style rifles and then there is full-auto/burst law-enforcement/military models.
If you just asking if an AR15, meaning any brand of SEMI-AUTO, post-ban or pre-ban AR15 style of rifle, whether it is Colt, ArmaLite, Bushmaster, RRA, etc, is legal to own in Cook county, the answer is YES, BUT different rules apply to the city of Chicago.
I live in Cook county, I legally own an ArmaLite M15A2 and a RRA LAR-15 carbine. Both AR15 rifles.
Currently, except for certain cities such as Chicago, there is no rules to own any type of rifle or handgun as long as it doesn't have full-auto or burst and it applies with current federal laws. Unless you are a dealer with an FFL.
Pre-ban hi-cap magazines are also allowed in Cook county as well as rest of IL.
As long as you have a FOID card, you'll be okay.