Xbox Live Communicator 'Puck' that used to fit inside of the controller
An old USB cable that you can cut up
Windows XP 32bit, Sorry, there are no drivers for XBox1 communicator under Vista.
Xbox Headset Drivers (thanks redcl0ud!)
Optional parts if you want to make it work with a 360 headset:
Dremel or side cutters to remove plastic
Xbox360 Headset (20 dollars)
You can also use a headset for an old cell phone if you like, most 3 conductor ones will work with no modification.
The XBox 1 controller was a USB device with a built in 2 port USB hub. You could put accessories in the 2 slots, one of which was the Live Communicator puck. A cool guy named RedCl0ud made Windows drivers for the controller, and sound drivers for Communicator puck too. The sound quality of the USB adapter is excellent and well suited for VOIP or Teamspeak. For a while I used to have the controller with the puck in it and used it that way with the PC, but it was kind of a mess having all of those wires and a big controller I wasn't using laying on the desk. So in this instructable, we eliminate the need for the controller's proprietary jack and install a USB cable directly to the puck. Optionally, you can remove the plastic around the jack as I did so you can use a 360 headset without modification. I find the 360 headset is immensely more comfortable compared to the original XBox1 headset, and doesn't break so easy! However, you are free to use any mic of your choosing, as long as it has the mini 2.5mm jack on it like a cell phone headset.
You can also use any communicator that originally worked with the XBox1, including aftermarket like the Logitech wireless unit. The drivers should work with all variants.