(430 ILCS 66/40) Sec. 40. Non-resident license applications.
(e) Nothing in this Act shall prohibit a non-resident from transporting a concealed firearm within his or her vehicle in Illinois, if the concealed firearm remains within his or her vehicle and the non-resident:
(1) is not prohibited from owning or possessing a firearm under federal law;
(2) is eligible to carry a firearm in public under the laws of his or her state or territory of residence, as evidenced by the possession of a concealed carry license or permit issued by his or her state of residence, if applicable; and
(3) is not in possession of a license under this Act.
If the non-resident leaves his or her vehicle unattended, he or she shall store the firearm within a locked vehicle or locked container within the vehicle in accordance with
subsection (b) of Section 65 of this Act.
http://www.ilga.gov/legislation/ilcs/ilcs3.asp?ActID=3497
(430 ILCS 65/2) (from Ch. 38, par. 83-2) - Sec. 2. Firearm Owner's Identification Card required; exceptions.
(b) The provisions of this Section regarding the possession of firearms, firearm ammunition, stun guns, and tasers do not apply to:
(9) Nonresidents whose firearms are unloaded and enclosed in a case;
(10) Nonresidents who are currently
licensed or registered to possess a firearm in their resident state;
http://www.ilga.gov/legislation/ilcs/ilcs3.asp?ActID=1657&ChapterID=39