Instructions
Call 1-800-4MYXBOX in order to reach Xbox Live Customer Support. You'll be asked for account info, active card info and the answer to your security question. Explain that you have been the victim of fraud on your Xbox Live account.
Await follow-up from Xbox Live Customer Support, which may take between 48 hours and 4 weeks. Customer Support will restore your account, as well as achievements lost due to the "Cheater" status caused by a hacked Xbox Live account. You'll be e-mailed an update on the restoration of your account to the e-mail address specified in your Account Settings.
Sign in to your Xbox Live account, and you'll be prompted to choose a new gamertag and password. These are the only two steps you have to take to set up your account again. When you've successfully logged in, you'll have to recreate your friends list, but your Achievements and any Points you had should be restored without the "Cheater" tag on your Gamerscore.