We thank Christopher Morgan of the Boston "We've Come for the Davenport" Chapter of the Robert Benchley Society and Steve Russell, practitioner of "Juggling, Comedy and the Art of Oomph!" (http://www.incapablehands.com/) for passing on this information about Benchley on Radio.
There are several examples of Robert Benchley's radio work available on Old Time Radio Cat at the website http://www.otrcat.com/. The site even offers a free sample of Bob Benchley on the Fred Allen Show. While you're on the site you can even buy Another Remarkable Wireless Talking-type Goon Show.
Other places to find Benchley on Radio are: