Just browsing casually at Illinois eviction laws state that you can't evict him prior to 10 days, and you certainly can't give him stipulations to stay the full 10 days.

You'd be hard pressed to find a judge to give you sympathy about his drinking problems when you've allowed it to happen this long.

You're pretty lucky he's not fighting this. The judge could tell you this isn't grounds for an eviction or he most likely has 30 days to leave the premise. I doubt a judge would evict someone without a 30 day notice (in Chicago of all places) for accidentally letting a dog out.