If you are willing to live in a studio, you can choose from several neighborhoods in the city from Rogers Park to Humboldt Park to even a couple of spots in Lakeview for 550. Several hoods in the South Side will also have studios for that price. And even have a small separate kitchen.
If you go around neighborhoods, and check out for rent signs, especially in Little Village area/Back of the Yards area, and honestly in most parts of the South and West Side, you can find people who rent basement/attic apartments with separate bedrooms for the 500 dollar range. These are not generally 'legal' with the city but if you are comfortable living there, tens of thousands of them are rented throughout Chicago.
If you want an actual home your only choice is to by a foreclosed property of which there are many in Chicago now that will have a total monthly payment under $550 a month. Just be 'flexible' on the neighborhood you want to live. It won't be Lincoln Park but it will be a house. Inquire with IHDA or chicagonsp.org for more info.
Come to the city. There's always options here. Avoid the hustlers and trust your instinct. Good luck