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The earliest I could find was by a John R. Norris in 1957 for a radio earpiece:
There are a lot of behind-the-ear headphone/microphone combos, but that's not quite what you're asking about. The first dedicated behind-the-ear headphone I found was Simeon Schreiber's 1988 "Bone Conduction Audio Listening Device and Method":
But importantly, the first patent I found that was actually assigned to a corporation was to Philip's 1997 "Wireless Ear-Worn Audio Device":
So long story short: I think the answer is the first marketer may have been Philips, but there are a lot of patents shortly after this assigned to Sony. I don't know who got to market first.
EDITS: Apologies for all the edits. It was my first time navigating the patent office's website.