The installation of Linux on Xbox is not supported by Microsoft. People argue that installing Linux on your Xbox does not promote piracy, and therefore the DMCA should not apply. Xbox-Linux.org states that it is not illegal to install Linux on your Xbox. However, it does void your warranty.
Looking further into the legality and ethics, you are running unsigned code on your Xbox by using exploits to install Linux. Is that enough to warrant Microsoft suing you? People have endlessly argued over whether this is legal/illegal or ethical/unethical in forums. The "Free-X" group released its exploit amid threats from Microsoft to sue them, but no known cases were filed. The exploit worked with older version of the Xbox dashboard software, which has since been fixed by Microsoft in its newer versions of the Dashboard software. With regard to Linux installation on Xbox, it seemed like Microsoft's main concern was with the installation promoting video game piracy. In addition, the methods listed in this project do not allow the Xbox to play pirated games.
Currently, it is known that Microsoft auto-installs fixes for the exploit when users connect to Xbox Live! While Microsoft does not have an official policy on the installation of Linux on the Xbox, they do release auto-installing fixes for every new exploit.
So our answer for now is: While we have not found any laws forbidding the installation of Linux on the Xbox, you are definitely voiding the warranty. Additionally, if your intention of modification is piracy, you are definitely trying to do something illegal-please look elsewhere and at your own risk!
Special things to note:
1) The Xbox can be a fully-powered PC at a fraction of the cost.
2) It is a cool thing to do.
3) You void the warranty by opening or installing software on the Xbox.