Quote Originally Posted by (625 ILCS 5/6‑105.1)
Sec. 6‑105.1. Temporary visitor's driver's license.
(a) The Secretary of State may issue a temporary visitor's driver's license to a foreign national who (i) resides in this State, (ii) is ineligible to obtain a social security number, and (iii) presents to the Secretary documentation, issued by United States Citizenship and Immigration Services, authorizing the person's presence in this country.
(b) A temporary visitor's driver's license is valid for 3 years, or for the period of time the individual is authorized to remain in this country, whichever ends sooner.
(c) The Secretary shall adopt rules for implementing this Section, including rules regarding the design and content of the temporary visitor's driver's license.
(Source: P.A. 93‑752, eff. 1‑1‑05.)
This is what I could find in the Illinois Vehicle Code regarding the Social Security Numbers. The problem is that they will complete the form in such a way as to create an adhesion. I understand the autority to drive on the highways comes from ability to cover accidents costs -- and insurance will only cover licensed drivers.

What if I don't have a legal name either?