As far as I know Illinois has no such law. If we do we citizens have not been informed of it and I have made no effort to find out what our laws are. Using a light at night is a no brainer. I've been running my headlight during the daytime in blinky mode since my accident earlier this year, but not on bike trails just on public roads. It seems like a good idea even though it is not 100% effective. I believe that Illinois motorcycles are required to burn their headlights all the time, either that or most modern motorcycles come set up with DRLs and riders don't bother to defeat them. Any state that requires daytime use of motorcycle headlights is game to require them for bicycles too, I suppose. Probably Big Nanny just hasn't thought of it yet....
Ken