Harris presents his arguments fairly well, but on this topic I don't agree with him at all.
His basic argument is hard determinism re-hashed. He says every event is either caused by a prior chain of cause and effect, or it's random.
I am still intrigued by why a determinist would believe in randomness, it seems completely contradictory to me. And he gives no justification in the lecture for why the only other option is physical cause and effect. He just accepts this as a given, missing the entire point of the argument for free will. Harris seems to look upon the brain as merely a physical machine, taking no account of consciousness and the power of reason at all.
It's a shame that Christopher Hitchens is no longer with us, he could point us in the direction to the most intelligent way of looking at the problem....