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I dont think a xbox has enough RAM to handle both something recoding a video into divx in the background and playing a game.
Lets not forget that the xbox can only have one process at a time so the idea of a background task is out of the question. But to be honest, the idea of just recording live tv is possible on 64mb of ram. All that would have to be done though is record the tv as a mpg file (mpeg 1 should be fine for normal tv and mpeg 2 for hdtv) and then just have the xbox convert it to divx once you hit stop.
You would just need a large hdd for it. <