No. You could travel through Chicago with it unloaded and locked in the trunk, but if Chicago is your destination point and you are not a law enforcement officer, even that manner of transport is illegal.It is a ridiculous local law which perpetuates a very high crime rate.
Better have it cased and in the trunk. Bring proof of ownership, your FOID card, and an order from your commanding officer requiring you to be armed. It really bothers me that you will have it in the city of Chicago, where handguns are banned. (Only criminals seem to be allowed to have gun.)
If it is broken down and in your trunk, if you are stopped and it is in your cabin and not broken down it s a felony - welcome to Chicago.
As long as you have it in the trunk of your car, it is legal, if you can legally own a firearm.