You cannot. Others can be played but not this one.
Check out this list for games that are compatable:
Wikipedia Version (I personally think this one is better):
http://en.wikipedia.org/wiki/List_of_Xbox_games_compatible_with_Xbox_360
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The Xbox 360 can play original Xbox games but the Xbox doesnt play Xbox 360 games.
Yes xbox elite's can play xbox 360 games
Yes, It Is Possible To Play Old Xbox Games On An Xbox 360, However, You Cannot Play Xbox 360 Games On An Original Xbox.
You can not play xbox 360 games on an original xbox, however you can play some original xbox games on an xbox 360 console.
No the PS2 does not play Xbox 360 games only the Xbox 360 plays the games for it.