One place you might start looking for properties in Chicago is the Chicago Housing Authority's site:
This page has a list of some of the properties in all parts of the city that work with tenants who have Housing Choice Voucher Program certificates.
In theory, any private property owner can accept a HCVP Certificate. In practice, many landlords either don't understand the program or don't understand its benefits.
This why I think the CHA site is a good place to start: you know you'll be contacting someone who knows how to work with a certificate holder. Of course, my colleague's'suggestion below to search for "Section 8" or "Housing Voucher" on Craig's List or another site also could get you the results you're seeking.
A REALTOR certainly could help you to find such properties; some REALTORS actually specialize in this area. Look for one that knows the area in which you want to live, and have them ask the tough questions for you!
Don Pasek, CIPS, TRC, ADPR
Omniterra Real Properties
However, i worked the area for a few years and have always been successful with criterias like yours.
Feel free to search my wesite and/or give me a call!