@Di F. what type of building is this and what area is this in? @Mark Ainley is definitely someone I would connect with. His company GC Realty manages a lot of units, and he has a great reputation. He also runs a meetup for property managers, so he knows people in areas he can't service.
Hey there @Di F. - There are probably thousands of property managers in Chicago - you will get what you pay for! Someone that charges a bit more will for sure save you money in the long run. Connect with Mark like Tom and John mentioned. A good property manager is worth it's weight in GOLD and deserves what they ask because it's a tough business.