Most Mic/Headsets have the red/white left/right jacks that interrupt the signal and redirect it to your Earphones, along with the green audio jack that plugs in.
So if you set your preferences so that the chat comes only through the headset, and not the speakers, then you have effectively separated the audio.
The trick then would be to record the 'speaker' audio somehow (on your stereo?) or through whatever device you send the 'speaker' audio to (the right and white jacks). This is one track.
Next from the green audio jack have that plugged into another device (laptop maybe?) and record it that way. This is the second track. The 'chat' track.
Now as per what Moliat says, the 'chat' track will also have the regular sound, but it will boost the chat and drop the background when someone speaks, and this would work out okay, and actually allow you to sync it better to the other audio when the time comes.
Now of course I'm talking here from the perspective of myself editing video (and audio) using Final Cut Pro on my Mac, with all the separate video and audio tracks to work with.