A treasure trove of rare and unique live jazz recordings have recently become publicly accessible; audio engineer William Savory recorded over 100 hours of live music played for the radio in the late 1930s, and the National Jazz Museum in Harlem now holds his formerly private collection (which came from Savoy's son, about an hour and a half west of Chicago). The Nation Jazz Museum in Harlem has some sound clips on their website here.
First heard the story on NPR (Aug. 20th story here), but the New York Times had the story before that (Aug. 16th full story here). Below is a little background video from the New York Times.
More sound clips, with informative short descriptions can be found on the NYT website here. Definitely listen to Blues Jam, the last one on the page, for an incredible 3 minutes of Fats Waller, Louis Armstrong, and Jack Teagarden: a truly joyful improvisation.