If you've spent any time trying to record or stream game play from Xbox One you've probably noticed that it's basically impossible to record party chat with great results. I've personally tried numerous work arounds including using splitters and running multiple microphones but none of the current crop of options has given me the results I'm looking for without being awkward.
Windows 10 however includes a new app called Xbox that makes recording Party Chat simple and provides great results. This article will walk you through the process of setting up Windows 10's Xbox app, OBS or Game Capture HD with an Elgato HD60 to record gameplay and Party Chat while keeping the game audio and chat audio reasonably or completely in sync. This method should work for any capture card but the HD60 is what I have experience with. The great part about this solution is it'll work with any headset (or even Kinect) without the need for a second microphone. That said, you can also use this setup to record Party Chat while using a local, higher quality mic option to record yourself without affecting how party members hear you. Remember that while using this setup to record Party Chat you're going to use up an additional party member slot in Party Chat and voice quality of yourself will be less than when using an external microphone.
This video shows the level of quality you can achieve using this method:
The basic setup no matter which capture software you use is the the same. You need to create an extra Xbox Live account that you can use on the PC. This user will join your existing party and simply listen in allowing you to record party chat audio. I'll refer to this user as the "recording user." Once you've created the new Xbox Live user start the Xbox app and login as that new user and then add your normal Gamertag as a friend. Now that user can join any existing parties that your regular Gamertag is a part of or start a new one. From there you'll find that the Party Chat audio is just part of your normal system audio allowing you to use your usual game recording or streaming software, such as OBS or Game Capture HD, to capture the audio.
When you are in a Party you'll see this while viewing your account in the Xbox app. From here you can easily join the Party.
You'll now be part of the party and all party chat will be output on your PC.
From here, click which capture setup you want to use: