Neither can I, despite the fact I'm registered, but once I change my ID later today I will be unable to vote until February.
Unless Illinois is different from Minnesota, you can do a walk-in and vote with your new address. Just be sure to bring the change of ID form you will have.
Edit to add that this is what I had to do 2 years ago when I got married and had a name change. Had to bring the old Drivers License along with the form I filled out at the DMV and was able to vote that way.
I am just finishing up getting my State ID changed, voter registration updated, getting my rent money taken of, and now headed back to the Metra at 1:35 PM.
Did you have to prove you where really you? I had state ID and it had expired but I still tried to use and the saleslady said it expired. I told her that I did not expired , I am still me. She did not buy that, so I guess when your state ID card expired you do too.
Strange you mention that, because when I got to the State Building, I realized that I had fogotten my lease agreement copy..... OOPS. However, I got bailed out by going to the bank and getting a bank statement with my current address on it (Thankfully I had the common sense to change it online the day I moved), so it worked out well. Plus, my state ID wasn't due to expire until 2020, anyhow. Now it'll expire in 2024.