I live in Evanston - I don't know if that's convenient for you or not - but here there are nursing homes that offer free CNA training. Presbyterian Homes is one of them and Resurrection also offers basic CNA training (I think it's free) at Saint Mary's downtown.
Don't quote me on this but I think in Illinois any nursing home receiving state assistance is required to offer free CNA training. You should call around. Now, there are a few downsides to going this route:
1. These programs aren't offered very often. Presbyterian Homes for example only does the free training twice a year and there's a lengthy interview process. They always have more applicants than slots.
2. Free programs take longer to complete. Think about it, as a CNA student doing clinicals you're free labor for the home or hospital. The longer they have you working for free, the more money they save by not paying someone to do the same job. It's hard to find reliable people who will do this sort of work for 9 bucks an hour. I think the PresHomes class lasts something like 2-3 months and it's five days a week from 9-3. As a stay-at-home mom with two young children, I couldn't keep that kind of schedule.
3. There are more people who want into these programs than there are slots. I called Resurrection and left messages at least five times and no one ever got back to me. Granted, I probably could have gone into their office and talked to someone but I wasn't in the mood to deal with it. Most of these programs have lengthy if not arduous application processes.
I don't know what your financial situation is like but if you're able to pay there's also the community college route. The school for my suburb is Oakton and they offer a CNA. Of course, there are downsides to this as well. It's about $900, including tuition, fees, books, etc. if you're in district. And it's long! 10 weeks if you go 9-3 five days a week and 16 weeks! if you go in the evenings.
Because I needed to finish my CNA asap to apply for a nursing program
I went with Career Training Center in north Chicago. They're relatively inexpensive - tuition is about $500 (plus book ($50), cpr ($20) and uniform ($20) and they offer a payment plan. It's a family operation - the nurse instructors are a mother-daughter team and a brother runs the office. Candice, my instructor, was one of the sweetest people that I've ever met. The best part was the program is only three days a week for five weeks and you can choose whether to go in the morning or evening.
There are a lot of options out there so I hope you find something you can do. Good luck.