I've looked into this and from what I can tell you need a letter stating you can't get a Social Security number in just about every state. Then you need a proof of address such as a phone bill with your name on it...a friend who states you'll be staying at his place for X number of months is probably good enough. In some states it is a felony to lie...something to do with terrorism I imagine. Anyway, if you go to the AMA website you'll be able to find a list of all the states and their requirements for getting a license.
Good luck and let me know what happens!