Registered under the laws of a foreign state (such as Delaware for example), does not eliminate your obligation to register your business in Illinois if you plan to operate in Illinois. And, even within Illinois, cities and townships can have different regulations regarding business licensing and operations. Failing to follow your local rules could inadvertently cost your business its limited liability protections.
And the horror stories you may have heard about violating federal employment laws are exacerbated when you factor in local laws and regulations. Many state and local laws have broader application than their federal counterparts and some have stricter enforcement provisions. It doesn't give a business owner any solace to know he/she followed the federal rules when a state agency comes in and assesses penalties.