One of the earliest commercial recordings of Bradbury stories is a 1962 LP featuring Burgess Meredith reading two stories: "There Will Come Soft Rains" and "Marionettes, Inc."
As far as I know, this has never been released on any other format. The LPs are not exactly rare - they pop up on eBay from time to time.
The estimable Zombie Astronaut, whose blog is a constant source of audio rareties, some classic, some just bizarre, has posted MP3 files of this LP. I don't know how long the link will stay active, so you should listen while you still can: click here.
For more information on Bradbury material released on tape or disc, see my list here.