He once stated this, for example:
Let me summarize my views on what modern evolutionary biology tells us loud and clear - and these are basically Darwin's views. There are no gods, no purposes, and no goal-directed forces of any kind. There is no life after death .... There is no ultimate foundation for ethics, no ultimate meaning in life, and no free will....Provine is saying that atheism is inconsistent with a belief in any of these, and readers of Viewpoint know that I agree with him, which is why I think that the only consistent position for an atheist is to be a nihilist about meaning and morality.
Provine himself is what most people would consider a "good guy", but I think there's a disconnect between the way he chooses to live his life and what he believes to be true. It's an inconsistency that I think many atheists like him have to accept because they simply can't, or don't want to, live consistently with the implications of their naturalistic worldview.
He recently spoke to a high school class on some of these matters (Where was the ACLU?). At around the 3:30 mark he addresses the subject of morality. Listen to what he says: His parents brought him up to get a good feeling from being kind, and that's how we all should raise our kids.
Well, yes, but this elides a very important question. If atheistic evolution is true what reason do we have for thinking that kindness is "good"? If someone was brought up to be cruel, as many are, why would that be bad? Would it be bad because we don't like it, or it doesn't give us a good feeling? Is kindness good because it gives some people a good feeling? Of course not. Whether we like or don't like something, whether it makes us feel good or bad, hardly makes something right or wrong.
As frank as he is about the implications of atheism, what Provine fails to acknowledge is that if atheistic darwinism is true then the logical ethical consequence is might-makes-right egoism. Provine would doubtless recoil from such an ethic himself, but his reasons for doing so would be purely a matter of subjective repugnance. What he can't say is that someone who embraces such an ethic is wrong.