Section 926A. Interstate transportation of firearms
Notwithstanding any other provision of any law or any rule or
regulation of a State or any political subdivision thereof, any
person who is not otherwise prohibited by this chapter from
transporting, shipping, or receiving a firearm shall be entitled to
transport a firearm for any lawful purpose from any place where he
may lawfully possess and carry such firearm to any other place
where he may lawfully possess and carry such firearm if, during
such transportation the firearm is unloaded, and neither the
firearm nor any ammunition being transported is readily accessible
or is directly accessible from the passenger compartment of such
transporting vehicle: Provided, That in the case of a vehicle
without a compartment separate from the driver's compartment the
firearm or ammunition shall be contained in a locked container
other than the glove compartment or console.
http://caselaw.lp.findlaw.com/casecode/uscodes/18/parts/i/chapters/44/sections/section_926a.html
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That's the actual statute...so legally you should be fine. BUT...that does not mean that you won't get raked over the coals. Some cities are very strict...mainly up north in the Chicago area....and although they can not supersede federal law...they can make your trip a bad one....if you run across any blogs or message boards where this is discussed, you will see the same advice I will give....stop at the border and lock the gun in a case, in the trunk. Of course you will also hear things such as...."The Peoples Republic of Illinois"....and words like...Fascist, Natzi and Commie are slung regularly.
For the record, yes I do this too....but I tend to avoid using the extreme right terminology, I confine my diatribe toward the commie angle...because I'm good at it....and I often throw in Yankee bastards for some flair.
I live near Cairo IL., which means I also live near KY, MO and KY laws are quite lax compared to those in IL, I don't know anyone that would recommend traveling into IL with a pistol, much less simply traveling into IL. At times I have to, because of work, and I always make sure all my lights are in working order, that I have nothing that could be used as a weapon in the truck...and I put on my stupid ass seat belt....MO, 10.00 fine...IL is 50.00 any others it jumps to 100.00.
I-57 is a major drug trafficking vein, the police are thick and unforgiving, I avoid it if possible.