No, it is illegal for people to keep wildlife as pets per the Illinois Wildlife Code (see below). For more information call Brian Clark with the Illinois Department of Natural Resources at (217) 782-6431 and select option 4.
"It is unlawful to take, possess, sell, or offer for sale, any such wild birds (dead or alive) and parts thereof (including their nests and eggs), or such wild mammals (dead or alive) and parts thereof, including their green hides, contrary to the provisions of the Illinois Wildlife Code".