I have a modchip (Xecutor Lite 2.3) on my xbox, and can play online with my PURCHASED games by turning off the modchip first. There's no way for MS to detect whether you have the modchip installed or not if you turn it off before turning on the xbox if you want to play on live. Then your xbox acts just like a normal xbox.
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I just remember that you can play many games with the modchip on if you use XBConnect -
http://www.xbconnect.com/ What this does is fools your xbox into thinking that your computer is another xbox. Then you connect to your computer via an xbox-link game, and then your computer communicates with other people's computers which are connected to their xboxes... basically, you can play xbox-link games over the internet. It works pretty well

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