Simply put, no you will not. Only on a peaceable journey that takes you through Chicago (meaning just that; passing through. Stopping or staying there with a handgun is a no no). Handguns not registered as of 1982? are banned in Czar Daley's People's Republic of Chicago for residents and anyone else who is not passing through. The only way you'd be legal with a handgun in the PRC is under the following conditions:
TITLE 18 PART I CHAPTER 44 Sec. 926A.
Sec. 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
Again, this applies only if you're passing through Chicago on a continuous and uninterrupted journey. I would suggest that you either leave your handgun at home or travel past Chicago and find yourself a hotel in Northwest Indiana if you must have your handgun with you.