Not there is a way and it doesn't requre a mod chip.
It allows all NTSC machines to play all NTSC games but no PAL games
surprisingly all PAL machines can also play NTSC games. It requires quick hands and flawless execution, and no I haven't tried it, but I'll try and dig up where I saw it.
But here is kind of what I remember:
Load up a regular "this region" game
Wait for game to show up, and hover the reomte over the start button
Eject the Disc and click start at the last possible second before the button is disabled
Insert "other region" Disc before system tried to reboot
If it works, it should load your "other region" under the copy protection of your "this region" game and you should be able to play the game normally.
Give it a shot, let us know if it works. Meanwhile I'll look up where I saw this at.
edit: never mind that was for playing GC games on the Wii