You may be able to start a policy with your Canadian license but most insurers would require you to get a US license, in this case from Illinois, within a short period of time for the insurance policy to remain in force. For a Chicago car insurance quote follow this link. Currently, all our Illinois carriers will require you have a current valid license to obtain insurance. 

To get information on how to acquire an Illinois State license, check with the IL DMV. Here it states that drivers moving to Illinois may use their valid driver's license from their home state or country for 90 days.

You may obtain an Illinois driver's license or identification card only if you are becoming a legal resident of Illinois. If you have a valid driver's license from another state or country, you may use it to drive in Illinois throughout your stay (if you do not plan to become a permanent resident of this state). Illinois does not recognize the international driver's license (IDP).