@Kevin Hunter- I’m sorry to hear this. I have unfortunately been in your situation more times than I would care to admit. I can’t back this up with any statistics, but I’d say about 90% to 95% of tenants don’t actually want any kind of derogatory marks on their record. Some might care more than others, but most want to avoid trouble.
You have a few options that don’t involve court, which should be the last resort in a place like Cook County. Cash for keys has already been mentioned and is a great way to get people off quickly and without as much hassle as going to court.
Depending on your relationship you could try and come to a peaceful arrangement. But it sounds like you might be past that point.
You can report them to the Credit Bureaus. There are several ways to do this. But I’ve gotten a number of people to come to their senses this way.
If all else fails, then I would file for an eviction. I had a similar situation last year. I served the tenant a 5 day notice and filed shortly after. The tenant was gone a few weeks later. She might be just seeing if you will call her bluff.