Instructions
Press the "Guide" button, followed by the "X" button.
Select your profile to sign in to it. Wait a moment as the console connects to LIVE.
Select your profile under the "My Xbox" menu on the dashboard.
Select "Edit Profile," followed by "Edit Sign-In Options."
Select "Available" under "Windows Live Messenger." Press "B" to save your changes. The next time you sign in to your profile, you will also be signed into Messenger.