I remember reading a few weeks ago about Alderman Reilly proposing an ordinance to increase the fines for private waste haulers that violate city regulations regarding trash collection hours. There are already restrictions in place (no earlier than 7AM, IIRC), but the fines are so minimal that the time restrictions are simply ignored and considered a cost of doing business. If I were you, I would talk to Ald. Fioretti and place a phone call to the offending businesses (be sure to mention the ordinance). If that doesn't get you anywhere, I would suggest more "creative" measures.
And (quick google search), here's the link to the article, if you are interested:
http://articles.chicagotribune.com/2012-12-11/news/chi-chicago-alderman-wants-crackdown-on-noisy-garbage-trucks-20121211_1_waste-haulers-chicago-alderman-garbage