Remember to change your driver's license to reflect your current address. At the same time, complete the proper forms to change your voter registration information.
If you do not have a driver's license and need to register to vote in Montgomery County (or change your address if you're already registered here), go to the Montgomery County website for complete information.
Change your car registration as soon as possible as well. Maryland law requires that all permanent residents with cars parked at their principal residence register their cars in the state within the first 30 days.
Please be aware that you should indicate that you live in Section 3 of the Village of Chevy Chase on your Maryland income tax return.