Three of my favorite science fiction novels are: Brave New World, 1984 and Fahrenheit 451. Thus, I was thrilled when one of my favorite sites which clues me into great new video / audio content posted to the net (Open Culture) had a post on Brave New World! You can listen to the author himself, Aldous Huxley narrate his book:
Apparently this broadcast was part of a CBS Radio Workshop Series (Wikipedia link) that took place between 1956 and 1957. You can download and listen to other programs from this series via the Internet Archive.