The 360 is region locked to either NTSC-U/J or PAL designated.
The developers of a game have a choice whether to region-lock their game, or to allow it to be region free. Some games are region-free while others are not, on the 360 this is designated by a flag in the XEX header. It is impossible to modify this without breaking the file's signature.
It is nearly impossible to change your 360's region to anything different, and impossible to make it region-free. The problem is that the 360's region is also stored as a flag in it's NAND which is locked by a cpu-key. An old exploit allowed access to the NAND, but seeing as how just about every console is now patched, you will be very lucky to find one that can still utilize the KK exploit (if you have played live anytime after August 2007, you can't).
In laymen's terms, no you can't. Unless you have a region-free game, or one designated to your region, it will be impossible. Even modchips won't work for you unless you somehow got your CPU key, or found a console that will be vulnerable to the timing attack (approximate cost of necessary hardware: $100).
