Do yourself a favor and buy this $15 headset instead of using the one that came with it. http://www.amazon.com/Turtle-Beach-Amplified-Headset-Devices/dp/B00KJGYA60/ref=sr_1_1?ie=UTF8&qid=1463498182&sr=8-1&keywords=turtle+beach+z11
If your controller has a 3.5mm jack built in, they should work right out of the box. Otherwise, you would need to buy the Xbox One Headset Adapter.
For $40 they are good. They will sound fine and have mic mute and volume control on the cable. Pretty nice feature if you have a 3.5mm jack controller and don't have a headset adapter. I had the z11 and this is basically the newer model. I was very happy with my z11 until I eventually got the XO Seven PRO. Amazon has the z11 for $16 if you are interested in that.
There's a thread on here for these on sale now. I picked up a pair myself. For 15 bucks it's a damn good deal. Ordered last night and will be here today it says apparently. Not wireless but yeah.
Linked in the xboxone reddit. Doesn't seem like a bad deal.... http://www.amazon.com/Turtle-Beach-Amplified-Headset-TBS-2145-011/dp/B00KJGYA60/ref=sr_1_1?ie=UTF8&qid=1449940531&sr=8-1&keywords=z11
Says they're "amplified" but the reviews say they work plugged directly to either XB/PS4 controller/headset adapter.
The Turtle Beach z11's are the one I use and they're still pretty good after 2 years of use. Their ear cups are very breathable and keep your ears from building up heat, and the mic is one of the best mics I've ever had on a headset.
The Turtle Beach Z11 is currently $16 on Amazon.
I just ordered mine the other day, and it seems to work alright so far, for 16 bucks.
Another great budget headset is the Polk Melee.
The melee is currently $34 in blue, if color doesn't matter to you. (other colors are more expensive, for whatever reason.)
The Z11's are open backed, while the Polk headphones are closed backed, if that is important to you.
Let me know if you'd like more information on either of those headsets, and good luck choosing!