The first Monday of March is that most Illinois of holidays, Pulaski Day. Most Cook County and Chicago government agencies and offices are closed. Chicago Public Schools will be open. Chicago Public Libraries are all closed. Most banks are open. Cook County courts are closed; federal courts are open. There will be mail delivery, and CTA and Metra will be running regular service.
It's a confusing mish-mash, so call ahead if you have any dealings with any city, county or state office.