According to the Illinois Secretary of State (SOS) those visiting the state may drive in Illinois with a valid license from your own country during your stay.

The IL SOS goes on to say that an international license is not recognized as a valid drivers license in Illinois. 

From this information it would appear that if you have a valid foreign license, your valid driver's license from India, you would be able to drive in Illinois but not with just the International Driving License (IDL) or International Driver's Permit (IDP).

For more information on what Illinois requires of you to drive in their state contact the IL SOS directly.