"A few" rather than one because there aren't any short audios that really do it any justice, nor alas has a great deal of Ian Hom, whose endearing and terrific performance was the whole point of bringing this up in the first place. There are some full one-hour episodes, but I don't think most people will want to sit through them just to find the "good parts". But you can still get a lot from these three selections I have below.
This first clip concerns the character of Faramir telling Frodo and Sam about the death of his brother Boromir. You might not be familiar with Faramir since he was left out of the film adaptation, al though Boromir was the character played by Sean Bean. This is mostly Farmir talking, but you'll hear bit of Frodo, as well as his ever-loyal aide Sam.
This latter is notable because, up until yesterday, I had no idea who had played Sam. And when I re-listened to the end of a long episode to hear the credits, what I heard was "William Nihee," which meant nothing to me. I happened to look up some information about the broadcast, and when I saw it in print, I was amazed. It was the wonderful actor -- Bill Nighy. (I'd always thought it was produced "Ni-gee.") For those who can't place the name, he was the burned-out rocker in Love, Actually, and Davy Jones in the Pirates of the Caribbean movies. And as iMDB.com notes, 123 other credits...
And for the fun of it, here is a song from the radio adaptation, sung by Sam -- played by Bill Nighy. (If you've only seen the movie, the novels are loaded with songs. Just the words, of course, but for radio they had music added by the wonderful composer Stephen Oliver.) The song is about the death of an ancient Elvin King, Gil-Galad