Not really, for Xbox Live-enabled gamertags. You can pay 800 Points to change the gamertag to something else, freeing up the first one for use on another profile. Or you can change the Live ID associated with the gamertag to something else, so the
first Live ID can be used on another gamertag.
(A local-only gamertag, which hasn't joined Xbox Live, can be deleted from your Xbox 360.)
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