If you are looking for housing, it is strongly suggested you apply for the Chicago Housing Authority waiting list. They have an extensive waiting list of Section 8 apartments where your rent is 30% of your income.
Below is a link to a spreadsheet of Chicago Housing Authority properties. When you select a CHA property, it may be a good idea to chose a property that has a lot of apartments. If you are looking for a two bedroom apartment, you may want to look for places that have a lot of two bedroom apartments. More apartments means more turnover, and possibly a shorter wait time.