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Oh yeah man. You can get it on any Live enabled 360. Just know your tag and the email it's linked to and you're good anywhere you want to be.
The only thing is, it's a huge pain in the ass to keep moving your gamertag around. You have to download your tag from xbox and it can take a while.
Ok, I have one Xbox360 in my basement that has my Xboxlive Gamertag ( Bluedemons..) Now if i were to get another xbox360 for christmas & put it upstairs, Can I recover BlueDemons on the upstairs one?