I've only had a quick look around, but it does look to be consistent with an Illinois license plate from 1961 or 62.
1961 was the first year that Illinois started using the two letters + four numbers format, and plates for that year were red with white lettering. 1962 plates were orange with white letters, which is also a possibility.
Earlier plates were all numeric, and the colour schemes of later ones don't match.
This is speculative, I know. Any experts on US license plates out there?