It certainly wasn't unusual for big band leaders to cover each other's hits during the swing era, but Glenn Miller's No. 1 hit A String of Pearls appears to have attracted more than the usual attention from his contemporaries.
Benny Goodman, Woody Herman and Harry James all recorded the tune. In fact, Goodman appears to have put out several versions over his lengthy career. The first came in 1942 (the same year Miller had his chart-topping hit) for Columbia's OKeh label.
This is the version you can listen to and download below. The MP3 is taken from a 1972 Reader's Digest box set called Million Dollar Memories.
A String of Pearls
While most Reader's Digest vinyl sets boasted superb sound quality, Million Dollar Memories was not one of them. An annoying and cheap sounding reverb was put on many of the monaural tracks, presumably to give them a "stereo" effect. But the result is a bit like listening to a speaker placed inside a trash can. Give this set a pass if you see it in your local thrift store.
Goodman completists will want Mosaic's seven-CD box set, The Columbia and OKeh Benny Goodman Orchestra Sessions, which of course includes A String of Pearls. It will set you back $119, a not unreasonable price for what you get.
A much cheaper two-CD selection of Goodman's Columbia recordings, The Essential Benny Goodman, is available from the usual suspects (including Amazon). However, A String of Pearls is not included. There is a Goodman version of A String of Pearls available for download at all of the major sources, but it sounds like a much later recording.
To close, here's a video dubbed from VHS of a Goodman-led band doing A String of Pearls. This lineup was assembled on April 10, 1959 for what appears to have been a TV broadcast.
More details of this video are available here.