According to the official UK distributor for Microsoft Studios and Xbox products named Gem, the box will now include a headset.
The Xbox One hardware bundle will now include the Xbox One console featuring a 500GB hard disk drive and Blu-ray player, the new version of Kinect, a HDMI cable, and a redesigned wireless controller in addition to a wired Chat Headset. This package will be available from an unspecified date in November 2013, with a recommended retail price (RRP) of £429 GBP.
So this is another good reversal from Microsoft regarding the Xbox One. It was weird that the PS4 was including one and not the Xbox One and I always thought it was silly that they expected the Kinect to be such an ideal way to communicate online that it could justify the omission of a headset.
Still, it's not an official statement so it remains to be seen if this will actually happen.
August 8, 2013 update
In a blog post published alongside a new Xbox One Day One edition unboxing video on Xbox Wire, Microsoft revealed several new details regarding its upcoming console and accessories as they unboxed the new machine, said to be one of 20 final-spec Xbox Ones in the world so far.
Most notably, the Xbox One Day One edition will include an Xbox One Chat Headset, reversing the policy Microsoft announced in June. (Note: IGN has confirmed with Microsoft that the Chat Headset will be included in every Xbox One and not just the limited-edition Day One versions of the console).