This is all the have:
Section 110.170 Weapons and Firearms - Display and Use
It shall be unlawful for any person, other than authorized peace officers, to display or use on Department-controlled lands, except as authorized by the Department on hunting (reference 17 Ill. Adm. Code 510, 530, 550, 570, 590, 650, 660, 670, 680, 690, 710, 715, 720, 730, and 740), field trials (reference 17 Ill. Adm. Code 910), target or special event areas, any gun including shotgun, rifle, pistol, revolver, air or BB gun, sling shot, bow and arrow, switchblade knife with spring loaded blade, throwing knife, tomahawk or throwing axe, or martial arts devices.
(Source: Amended at 24 Ill. Reg. 12556, effective August 7, 2000)
Since hunting (in Season) is allowed, and I see no specific prohibition from firearms (not displayed or used) on the property, I would think that a properly cased and unloaded firearm would not be a violation of any rule.
Perhaps a call to the local authority would be the best bet though...
dnr.state.il.us/legal/110.htm