Xbox One controller update required for stereo headset adapter
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Xbox One's March firmware won't prepare your console to use the stereo headset adapter; you'll need to update the controller itself for that.
The Xbox One stereo headset adapter ships with the Xbox One stereo headset or separately for use with third-party and legacy headsets.
In order to get it to work, you'll have to update your Xbox One controller - not just your console.
Updating seems pretty simple - connect to Xbox Live, plug the adapter into your controller, and plug the controller into the console via its USB cable, then follow the prompts.
If you have any trouble with it, Xbox Support has a detailed, illustrated step-by-step guide including troubleshooting.