I have not read Harris' book, but I'm skeptical. I doubt there's any reasonable disagreement that science can inform our values by, for example, helping us understand potential consequences of our actions or by helping us understand our own brains and how we arrive at our basic values.

Likewise our values can help to inform science by developing common rules for the ethics of animal experiments and the requirements for informed consent, for example.

In neither of these cases is science defining our values or our morality.

Harris' book is not on my "to read" list, but I do plan to watch his TED talks video some time to get a first hand gist of his argument. It could be that he's not saying what it sounds like he's saying. Or it could be that he offers some new argument or evidence for his opinion.