"Microsoft has informed its partners in the Xbox One console launch that the Xbox One Headset Adapter, being built by Microsoft and provided to Turtle Beach for inclusion with new gaming headsets, will not be available until early 2014. Both companies will leverage the additional time to build supply to meet anticipated high-demand when the headsets launch," the press release states.
Xbox Live won't be silent on launch, mind you; an unboxing video from Microsoft's Larry Hryb (aka: Major Nelson) showed that the Microsoft wired headset will be included with both regular and Day One Edition consoles. Prepare accordingly.
The Xbox One isn't the only system with headset compatibility issues. According to a report from Game Informer, USB headsets will not work with the PlayStation 4 at launch, and the Turtle Beach support page notes that although PS4 users can receive game audio using a digital optical connection, you'll need a headset with a mobile adapter connection to chat.