Kmeyer,
Here's a link to the Illinois Newspaper Database.
http://www.library.illinois.edu/inp/database.phpPut in Chicago in the search parameter and you'll get a long list of newspapers and where they can be accessed.
Some of the newspapers were neighborhood newspapers, so in order to determine the appropriate one I'd have to know where your family lived in Chicago (north side or south side). I don't think obituaries were as common in the early 1930's as they became just a few years later, especially for poor immigrants.