Just had a chat with a "support" agent. The Kinect chat feature IS NOT supported on Xbox One. It works perfectly well with Xbox 360.
The agent tried to tell me this was a fault of Microsoft, until I pointed out the Kinect chat on Xbox One worked perfectly well with Forza, Skype, BF4.
My issue was immediately passed on to the team that deals with these things (the bin), and I was told to use the mono xbox one headset, and forego stereo surround in my headphones through the optical, if i wanted to chat to people during the game. I asked if I could downgrade to the 360 version again. Pretty sure I could hear him laughing.
Merry Xmas Activision!! May your fantastic customer service run well into the nearest spike trap.