Can a Chicago Landlord ask a potential tenants immigration status

[Adam Sporinsky]

I have a possible tenant that called and asked if they can apply if they only have an ITIN number and no SSN.  Does anyone know if it would be a violation of any Illinois, Federal or Chicago laws to find out if they have a visa of any kind or are here illegally?

Mostly, I won't be able to do a credit report or background check, but if they have a valid visa from the US they have already passed some amount of background screening for entry to the country, if they have not got a visa then I would be out of luck other than doing a background check with name and DOB which could be difficult.

Anyone have any experience renting to people in this situation or advice on whether to/not to consider this type of applicant?