Although most U.S. states do not allow someone who was born in a country other than the U.S. and who has no legal immigration status here to obtain a driver's license, Illinois is an exception. (The short term for the status of the person described here is "undocumented." You might also hear the more colloquial "illegal alien.") Undocumented foreign-born persons in Illinois can request what's called a "Temporary Visitor Driver's License" or TVDL. This is based on a law passed in 2013, commonly referred to as SB 957.
If you are an undocumented person living in Illinois, you'll want to read this article, which explains the state's rules on getting a temporary driver's license and outlines the steps in applying for it.
Unfortunately, getting an Illinois TVDL does NOT give you any sort of legal status in the United States. Only the U.S. federal government has the power to legalize a foreign-born person's U.S. immigration status—no single state can do that.
What getting an Illinois driver's license does mean, however, is that you are allowed to operate a vehicle within the state and to carry a card proving that fact. That's definitely a benefit if you will be operating a car and don't want to risk arrest for doing so without a license (which could be a swift path to removal, otherwise known as deportation from the United States.)
But you cannot use your Illinois license either for federal identification purposes, to show to an employer, or to vote in U.S. elections.
The Illinois driver's license available to undocumented persons expires after three years. You can get another TVDL, but it won't be automatic, nor as easy as for people renewing regular licenses. You will basically have to apply all over again, as if doing so for the first time. (For a comparison of TVDLs and regular licenses, Illinois offers a handy comparison sheet.)
To be eligible for an Illinois driver's license as an undocumented person, you must:
Be prepared to gather a number of documents in order to prove the above.
In order to request a TVDL, you will need to go in person to an Illinois Secretary of State facility. There, you can submit a Verification of Residency Form, which you can download online and fill out in advance. In addition, you'll need to present documents proving your eligibility, as described on the Illinois Secretary of State's list of "acceptable identity documents."
For example, you could present your unexpired foreign passport to prove your foreign citizenship and signature (Part A of their list); your foreign birth certificate to prove your date of birth (though it won't be enough by itself, so you'd need a second item from Part B of the list, such as a certified school transcript or a U.S. visa); a declaration that you can't get an SSN (to satisfy Part C of the list); and a rental agreement or utility bill showing where you've lived (for Part D of the list).
You will also have your photo taken while you're at the licensing office.
If your application is successful, a TVDL will be mailed to you within a few weeks.
Your license will look similar to a regular Illinois driver's license, but with some important differences. For one, it will say "TVDL" at the top, as well as, "Not valid for identification." Strange as it might seem to have a photo identity card that says it's not valid for identification, this refers mostly to the fact that it's not considered valid for federal identification purposes, for instance if you were to travel on a commercial flight.
You might understandably be concerned that anyone looking at your TVDL might guess that you are not a U.S. citizen, and don't have any lawful immigration status at all. One thing in your favor, however, is that non-citizens who are lawfully in the U.S. on a visa would also request this type of visa.
The Illinois Secretary of State website contains detailed information on eligibility and the application process for a TVDL.