If you have the standard Xbox One controller (the one that came with your Xbox upon purchase), you'll need to get a separate stereo headset adapter. However, if you have an Xbox One controller with a 3.5mm audio jack, you can plug your headset directly into your controller.
For the Xbox Series X controllers that came with the Xbox Series X package, there's a dedicated 3.5mm audio port by default. The same applies to Xbox Wireless Controllers, Xbox Elite Wireless Controllers, Xbox Adaptive Controllers, Turtle Beach Recon Xbox Wired Controller, Nacon Pro Compact Controller, and other controllers you can add as Xbox accessories.
If you're scouting for a Xbox controller, check the specs for audio ports to ensure you can use a headset without an adapter.