I've read a few work-arounds for this, but they all seem a little involved. This post from Sly One on the Ableton forums sounds like a much cleaner method:
http://forum.ableton.com/viewtopic.php?f=4&t=146878
I would add that setting the BPM LED to display note stealing might be useful to make sure you're not losing anything by recording all your parts at once. (On the other hand if you can't hear it, it's not a problem, eh?)