Hi D.,
This answer comes mainly from my experience as owner/director of a home-based business offering school and child care info, both online (www.metroprofiles.com) and in print (Child Care Connections).
Many (but not all) child care centers offer part-time options. With a few exceptions (care for less than a given number of children, I believe 3 is the limit), child care homes must be licensed to operate legally. There are several child care resource & referral agencies (CCR&R) in the greater Chicago area that can help you if you are looking for a day care home situation (which one you call depends on what county you live in).
If you would like to contact me privately, you can email me at ____@____.com or call me at ###-###-####. Hope this helps
S. Redfern