Call the DMV first (1-800 252-8980)and have them check the vin to make sure it's never been registered in IL. If it hasn't then you need a bill of sale and a 65 bucks, proof of insurance and taxes for the plates (35ish??).
I'm waiting for eeyore to give me my bill of sale so I can do the same thing.
If you don't have the bill of sale then you need to post a 1.5 bond of value and provide a estimate and a sworn statement of where you obtained the moped.