From Page 12 of the Illinois Hunting and Trapping Digest 2018/2019.....

It's in .pdf form on the dnr.illinois.gov website.

Can I use a center fire rifle for hunting in Illinois? Or handguns?
A: The following species may be harvested with a rifle or handgun: coyote, striped
skunk, woodchuck, squirrel, rabbit, raccoon, opossum and red and gray fox. We
do not regulate the caliber of handgun or rifle that may be used, except on state owned
or managed areas, which normally allow only the use of shotguns or .22
caliber rifles. Squirrel, furbearers and woodchuck hunters may use a .17 caliber
rifle on some state-owned or managed areas. No rifles may be possessed in the
field, however, during firearm deer season except that trappers may carry a .22
rifle to dispatch animals during firearm deer season. Certain handguns are lawful
for deer hunting.
At all times when in possession of firearms, hunters must comply with all firearms
regulations as outlined in the Illinois Criminal Code.