In indian you should have no problem, I believe they honor all states permits...Ill is a different story right now. They are going thru a lot of changes, I have read but not confirmed that out of state people can have a loaded gun in there car as of last night, but again I can not confirm that. Locked in your trunk with ammo seperate should make you safe for now...are you planning on making Chicago your destination or way thru?. That may be a little bit different responce.
Here is a good site to help you out
http://www.handgunlaw.us/
this was on Handgun law site under Ill
Section 40
(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; 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.
Subsection (b) of Section 65 States:
(b) Notwithstanding subsections (a), (a-5), and (a-10) of this Section except under paragraph (22) or (23) of subsection (a), any licensee prohibited from carrying a concealed firearm into the parking area of a prohibited location specified in subsection (a), (a-5), or (a-10) of this Section shall be permitted to carry a concealed firearm on or about his or her person within a vehicle into the parking area and may store a firearm or ammunition concealed in a case within a locked vehicle or locked container out of plain view within the vehicle in the parking area. A licensee may carry a concealed firearm in the immediate area surrounding his or her vehicle within a prohibited parking lot area only for the limited purpose of storing or retrieving a firearm within the vehicle's
trunk, provided the licensee ensures the concealed firearm is unloaded prior to exiting the vehicle. For purposes of this subsection, "case" includes a glove compartment or console that completely encloses the concealed firearm or ammunition, the trunk of the vehicle, or a firearm carrying box, shipping box, or other container.
Note: Handgunlaw.us is not sure this allows you to Carry a Loaded Firearm in your vehicle while traveling through Illinois. The law does mention his or her state of residence or territory and has a valid permit/license to carry a firearm from your state/territory of residence. Until more information becomes available I would not carry a loaded firearm in a vehicle while traveling through Illinois.