There's a very easy way to mod your 360 and still be able to use live. You have to get a mod with an "on/off" switch so you can turn it off before you connect to live. That way you can just disconnect your 360 and turn the chip on when you want to play imported games. Obviously, this means that you will not be able to play the games online, but they're programmed to connect to US servers anyways.
This is no different then flashing the drive yourself and using custom firmware though.
There's a popular custom firmware called iextreme, which does pretty much everything that does, and doesn't require soldering. Unfortunately, the only way to play region free games is if the game is patched or region unlocked like DS said(as far as I know). I know there are people who play region free games on their custom Xbox 360, but the game needs to be unlocked or something. As far as playing a game on live, all you need to do is stealth the game. Stealth pretty much eliminates all of the code that allows Microsoft to detect you playing on live with that specific game(but that is a whole separate issue and involves pirating =( ). As long as you know what you're doing, you'll be fine. Oh, and just disconnect your ethernet cord from the back of the Xbox 360 when you want to play a game offline.
It's a waste of money to buy a chip, since flashing the drive is the same thing.
Either way you go about it though, there's no guarantee on your safety with live. A modchip can still be detected, as well as custom firmware. Not to mention the huge software update coming up, I would wait until it's released before trying anything.