Many scientists say that the American physiologist Benjamin Libet demonstrated in the 1980s that we have no free will. It was already known that electrical activity builds up in a person’s brain before she, for example, moves her hand; Libet showed that this buildup occurs before the person consciously makes a decision to move. The conscious experience of deciding to act, which we usually associate with free will, appears to be an add-on, a post hoc reconstruction of events that occurs after the brain has already set the act in motion.
This could only demonstrate that there is no such thing as free will if a person is a distinct entity from her brain--as though the brain "decides for her" what she will do, while the "person" is merely carried along for the ride.
That's absurd, of course. The brain is the person, or anyway the most substantial part of what we'd consider the person to be, so when your brain makes a decision, you are making that decision. If consciousness is a post-hoc reconstruction of mental processes, then so much for consciousness--and if your conception of free will depends on consciousness not looking like that, then so much for free will, but it doesn't have to be that way.