It depends on what the state of IL DMV rules are but after the REAL ID Act, a federal law was passed, many if by now not all state DMV's have become very stringent in the issuances of state ID's and DL's and usually will only issue documents for the validity of your immigration credentials, i.e. I-94 of your L-1 or the visa validity/ I would probably stick with the NY DL valid until 2015.
Check with the Illinois Secretary of State (www.cyberdriveillinois.com). Most of the information is available online, and if not stop by one of the offices. There are actually very efficient and it will not take much time to get an answer straight from the source.
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