As far as I know Best to check as there were some days in December but normally Tuesdays are free for Illinois residents. Need an I'd driver's license to prove.
Chicago History Museum. Free every Tuesday to Illinois residents between 12:30–7:30pm. Also free on holidays: January 16, February 20, March 4 and July 4. Free for children 12 and younger daily, and Illinois residents enjoy free admission during Illinois Resident Discount Days.Sep 5, 2017
Also, If you have a Bank of America every first Sunday of the month is free, even if you aren't IL resident.
Free every Tuesday to IL residents. It is free to IL residents on certain holidays. Proof of residency may be required.
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