Xbox One doesn't include a packed-in headset accessory, Microsoft has confirmed. The tech titan told Ars Technica that the next-gen consoles' official monaural headset, which plugs into an Xbox One controller much like its 360 predecessor, is sold separately.
For comparison's sake, PS4 comes bundled with a monaural earbud and in-line microphone. On the other hand, it doesn't come with the Kinect equivalent PlayStation Eye (sold separately for $60), while Xbox One packs in its camera-and-microphone device. Microsoft has stressed Kinect's ability to isolate voices from background noise and positioned it as a all-in-one solution for video and audio chatting.
If you'd prefer your whole living room doesn't hear the mind-boggling awfulness of Xbox Live voice chat, however, you're welcome to buy your own basic headset or (likely pricier) officially sanctioned third-party model.
The official Xbox 360 headset costs $20 if it doesn't come in your preferred bundle, so we'd expect its successor to retail around there.