Friends and foes of the intuitive and commonsense view that humans have libertarian freedom of the will all agree that it is, on the face of it, incompatible with materialism. If the mind just is the brain and the brain just is a material object subject to the laws of physics, our thoughts and intentions would seem to be the result of causal forces which predate us and over which we have no control. Free will, on this view, is an illusion.
There are three points to note.
The first: John Searle has written that the experience of free will is so compelling that people cannot act as though it is an illusion even if it is one. Hoffman and Rosenkrantz, in another connection, have said something significant to the dispute. They take the view that if something belongs to a universal and commonsense ontology, “then there is a prima facie presumption in favour of its reality. Those who deny its existence assume the burden of proof.” Swinburne has formalised these ideas into a basic principle of epistemology which he calls The Principle of Credulity: We should, in the absence of compelling evidence to the contrary, believe that things are the way they seem to be.
The second: There is no such compelling evidence against the view that humans have libertarian freedom of the will. The laws of Quantum Theory, notes Swinburne, are probabilistic. And while, in general, indeterministic behaviour on the small scale averages out to produce deterministic behaviour on the large scale, “it is possible to have devices that multiply small-scale indeterminacies so that a small variation in the behaviour of one atom can have a large scale effect.” Consider, for instance, an atomic bomb designed to detonate if and only if a certain carbon 14 atom decays within an hour. This would qualify as a “multiplying system,” since it relays indeterminacy on the small scale into the large scale, while a block of radioactive carbon would be an “averaging system,” since it averages out indeterminacy on the small scale to produce determinacy on the large scale. The brain, notably, is the most complex physical system known to science. And because it, “causes conscious events and its states are caused by conscious events,” so, clearly, “laws of a very different kind govern the brain from those that govern all other physical states.” It is possible that the brain is a multiplying system rather than an averaging system. And for this reason, “it is widely believed that Quantum Theory rules out physical determinism.” 
The third and final point is of great relevance to the first. There is in principle no possible evidence that could produce a justified belief in determinism because free will is a prerequisite to the formation of justified belief of every kind—including justified belief in determinism itself. To understand this last point consider the plight of a neuroscientist who seeks to establish that determinism is true. To complete his task he must make observations, discern a pattern, formulate a generalisation and infer a theory. All this relies on rational adjudication, memory and intention. But if determinism is true, these mental operations and their results have no rational content. His belief in determinism is, ex hypothesi, not caused by the apprehension of reasons but produced by a brain state that is itself determined by extramental forces. Justified belief in determinism therefore requires that determinism is false and so suffers from self-referential incoherence.
It follows from the combination of all these points (the compelling experience of free will, the Principle of Credulity, the lack of evidence and the a priori impossibility of justified belief in determinism) that we are rationally obligated to affirm libertarian freedom of the will.
What is the relevance of all this to theism? Since the Bible teaches that God, an immaterial spirit, created man in his image, Abrahamic theists have a priori grounds for expecting certain properties that resist reduction to the material to be instantiated in man if God exists. It is no surprise on theism that our most novel and essential property, our mental life, should resist a materialistic explanation.  Free will, in particular, is provocatively suggestive of the imago dei since if man exercises libertarian causation he instantiates in miniature the principle of uncaused causation imputed to God in classical theism. 
 Moreover, recent evidence appears to confirm that human beings exercise free will. As the British neuroscientist Chris Frith reported in a recent interview,
There is a slew of experiments around these days asking, “What happens to people if you tell them that they don’t have free will?” which you do by saying, “Francis Crick, who is the cleverest scientist around, wrote this thing saying, ‘All sensible people now know free will doesn’t exist.’” If you tell people they don’t have free will and they believe you then they are more likely to cheat on exams; they become more selfish. And, more compelling to me, is that their behaviour in reaction time tasks changes. Normally in reaction time tasks you slow down after you make an error (which is due to some monitoring of your behaviour in taking account of this) but you get less slowing down after being told that free will doesn’t exist—presumably because they have lost their faith in top-down control. And it even changes the amplitude of readiness potential in the brain, which of course was what Libbit was measuring in his famous anti-free will task. I think this is fascinating because basically, this is an example of top-down control, what people telling you influencing how your brain works, which is what free will is all about. So that telling people that they don’t have free will actually demonstrates that we do.
 For a discussion of all five mental properties that resist reduction to the physical, see here.