Somebody who had the Xbox development kit (software and the real debug version of the xbox hardward) was able to port Mame and put up a page about it. He basically said "it could be done", but he wasn't going to release it (his code couldn't run the non-developement xbox hardware anyway).
Now with the latest Linux/Xbox developments, you could get the hack chip installed (voiding the warrenty), loading linux on it, and then just downloading/compiling mame and it should work. But outside that, there is currently no version of linux of mame which will run natively on the xbox.
-Dave