IL state has a Schedule NR, which you need to attach to the IL-1040.

The issue is that if you want to e-file the IL return, you need to go to the Federal Info worksheet - Part IV - Filing Information section, Electronic Filing, and where it says 'Select state returns to electronically file' (see below). When you click on the drop down menu, the installed state should appear, but for Illinois, doesn't. 

It's odd, as on the Proseries Basic version, there is no problem, but Proseries Basic just doesn't offer the 1040NR Federal, so, using Proseries Professional.