Unlike Xbox 360, Xbox One will not include the headset as a pack-in accessory. Because Xbox One includes Kinect, gamers will be able to use that for chat instead. However, should you want a more intimate trash-talking experience whilst online, a new Xbox One headset will be sold separately.
Microsoft confirmed the omission to Ars Technica, stating that Kinect features "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."
By comparison, PS4 will include a headset in the box. However, it doesn't look like something you have to get too excited about: