It's possible to tweet your Xbox Live activity and status to Twitter fully automatically.
To accomplish this, you can make use of the following sites.

I make use of the following sites:

Xbox Live Nation
To make use of the Live twitter.com integration tool you must be a registered user of Xbox Live Nation.
Registration is free.

When you make use of there twitter tool, the tweets looks like:

Xboxtweet

Xboxtweet is antoher site that you can use. This site needs no registration, they make use of  OAth (An open protocol to allow secure API authorization).
You give the API access to post tweets, the only need your Twitter and Xbox Live account.
See the Xboxtweet FAQ site for more info.

Twee60

Twee60 is also a site that can tweet your Xbox Live Status. I don't have no experience with this site.