Microsoft was heavily criticized for not only refusing to include a headset with Xbox One, but removing compatibility with any current-gen headsets. Xbox One controllers use a proprietary port, which Microsoft argues offers "higher data transfer speed between the controller and the console." For online chat with Xbox One, Microsoft has given gamers two solutions: use Kinect's built-in microphone, or shell out $25 for a proprietary first-party headset.
If those options still aren't palpable, here's a third choice: buy an adapter that enables use of current-gen headsets.
When grilled about Xbox One's lack of support for 360 headsets, a Microsoft rep said "Xbox plans to develop solutions in the near future to allow consumers to connect many brands of wired gaming headsets to the Wireless Controller for gaming and chat audio." That solution is an accessory (sold separately) that will let you use legacy audio hardware.
Of course, the question remains: how much will it cost? If it's near the $25 asking price of the Xbox One headset, this solution doesn't seem like much of a fix at all.