According to Microsoft, "Xbox One does not include a pack-in headset accessory. Each Xbox One includes the new Kinect sensor, with a highly sensitive multi-array microphones designed to enable voice inputs and chat as a system-level capability, both in-game and with Skype and other experiences."
For gamers picky enough to want a headset, Xbox One headsets can be bought separately at.
The original Xbox 360 did not come with a headset. Some of the later bundles did include one.