Hi Cassandra. Congratulations on your pregnancy! In Illinois, there are no free standing birthing centers as direct entry (aka professional) mdwives do not have a legal standing. Having said that many families are still choosing to safely birth at home. There are a handful of certified nurse midwives that attend homebirths so if you're interested I can give you their info. They work with most insurance plans and can help you navigate through the paperwork.
If you're not comfortable with a homebirth then your next best option is having a mdwife (or midwife practice) within a hospital that is known to be as naturally minded as possible. I am a doula and I've worked with alot of midwife and OB practices at different hospitals and I have to totally agree that West Suburban Hospital in Oak Park and Swedish Covenant Hospital are far best the most naturally minded hospitals. I know they are not located in near southeast Chicago but realistically given that this is your first pregnancy you would have more than plenty of time to get to the hospital at the time of birth and would be worth it.
I once had a client who would drive in all the way from Kenosha Wisconsin to see the midwives at West Suburban and had a beautiful and peaceful waterbirth.
If you strongly prefer someone in your area let me know and I can suggest a few places but I urge you to visit and talk to either West Suburban or Swedish. Or if you're open to homebirthing I can give you a few nurse midwife referrals too.
I wish you lots of good health and joy during this wonderful time!
A.