Philosophers since the time of Socrates have rejected this approach (known as divine command theory) on the grounds that, in the absence of any independent set of reasons, God's commands would turn out to be completely arbitrary, and hence objective perhaps -whatever that means- but certainly not moral.
Now, while the discussion below provides lots of great food for thought worth pondering, it seems to me that by defining morality in their own particular ways (a move that's ultimately inescapable), both philosophers were probably preaching to their respective choirs, and that the chances either of them might have gained new supporters who didn't already agree with their take on the issue are probably nil.
I'd say the debate was very interesting, and even though I tend to lean more in Harris' direction, I'm not sure either speaker won the day on the basis of the relevant arguments alone...
Both managed to undermine each other's position rather well, but neither managed to overcome such blows once they were dealt, and both were more than happy to go off on tangents irrelevant to the main point of discussion while still managing to provide thought-provoking arguments.
I'd declare the debate a draw, with both participants seriously injured by the other. Perhaps it was an act of martyrdom undertaken for our sake :)
I'll be posting more interesting talks on this topic soon, but in the meantime, here is philosopher Peter Singer with some thoughts on the subject.