Due to the changes that Microsoft made to the Xbox One controller, 360 headset peripherals will no longer be functional. Essentially, the talk function on current-generation headsets would be rendered useless.
The Xbox One will also not be coming with a headset, unlike its predecessor. Microsoft's reasoning for this was that the Xbox One came packaged with a Kinect, which it believes is suitable for in-game voice chat for customers.
However, Microsoft has now announced that it will be working on adapters for 360 headsets to work with the Xbox One. "We are working to develop an adapter for current wired headsets to connect. More details as we approach launch," stated a Microsoft representative via the Xbox Support Twitter.
Unfortunately, the company hasn't released any more details on the adapters, such as whether or not they will be available as an accessory to buy at retail or if they will arrive packaged with the console itself.