I live in NE Kansas.  I saw one cross the road 2 years ago.  I know what a cougar looks like, I lived in Nevada many years.  I have also seen tracks along stream beads, like I said I have seen them before.  
Last week I was listening to local PBS station in Kansas city and numerous people reported seeing them, mostly farmers, so I have no doubt they are in Illinois.
They follow the deer, and there is an explosion of deer population around here.