Does Neuroscience Threaten Free Will?

Some neuroscientists go so far as to claim that there is simply no such thing as free will. The feeling we sometimes have of freely choosing is just an illusion, a trick of the mind, they say. We might think we are making free choices, but, in fact, the choice has already been made before we become aware of it. But what, you might ask, would a neuroscientist know about the philosophical problem of free will?