I'm a single grandma / foster mom to my two little granddaughters. I live in Carol Stream. I have two groups to tell you about: We've been working at getting a group started in my church. We've met twice (once monthly) so far, and both of those have been in Carol Stream, but with the goal to move it around monthly to accommodate those that live further away (we have someone that lives in Montgomery and at least two in Aurora). It is a Bible based group (our goal is to help one another to raise our kids in a way that is pleasing to God). Let me know if you'd be interested, and I can give you more details. It's just a small group right now, we only have about 12 single moms in my church, and not all have attended.
If you're not interested in a Bible-based group, I found a single mom's group in either Bloomingdale or Glendale Heights on meetup.com, however, I've not attended anything yet, so I have nothing to share with you about it.