Neuroscientist Sam Harris' Statement "Free Will is an Illusion" is Logically Self-Contradictory

See neuroscientist Sam Harris' Youtube videoon the subject of the "illusion of free will" here. Below is a response to Mr. Harris:

Dear Mr. Harris:

Is your belief that “free will is an illusion” based on logic, or brain chemistry? If it is based on logic, then congratulations! You alone, among all humans who have ever lived, actually possesses the free will to veto the dictates of your own brain chemistry. Can I have your autograph?

If, on the other hand, your belief is based on brain chemistry, then it is not based on logic and therefore there is no particular reason to suppose it’s true (adaptive, perhaps, but not reliably true, even if your brain chemistry compels you to believe it’s true). The assertion that “free will is an illusion”, then, is a self-refuting statement based on intellectual vanity. Even if there is no such thing as free will, there is no way we could ever know that. We could only “believe” it, and even then only for as long as our brain chemistry compels us to believe it.