^ That's not as easy as you'd expect.
There are better copies of this floating around.
AAAAAND, it's actually not one of the earliest. Almost all of Kaye Ballard's flops have recordings (Golden Apple, Royal Flush, and Rueben, Rueben), there are two live songs from the OLC of Guys and Dolls, and there is an audio of Carol Channing in the 1952 tour of Gentlemen Prefer Blondes.
In fact, I think the earliest is a recording (albeit not a great one) of the Ziegfeld Follies of 1936.
http://www.youtube.com/huskcharmer