Please keep in mind that the following address has not been confirmed by official sources so I am not sure if it will reach Scarlett or if she even reads her fan mail. I have never heard of anyone getting a reply back.
If you will still attemp writing, include a properly stamped and self addressed envelope (US) or several International Reply Coupons (international) if you are hoping for a reply. Needless to say, your letter should be respective and not overtly long.
c/o William Morris Agency
One William Morris Place
Beverly Hills, CA 90212