I have an Xbox One S, and the controller I use is the default one that came with it (the revised version of the Xbox One controller with a built-in universal headphone jack and slightly cheaper, creakier construction.) Recently, the right stick has begun randomly drifting to the left (even after adjusting the dead zones as high as they could go on Halo: The Master Chief Collection.) Is this a problem with all Xbox One controllers? How are third party offerings if so?
I have two of the same controllers as you; sometimes they'll randomly drift off to the side as well. A little bit of rough-housing with the stick works for me, but it's probably a sign the controller is getting worn out.
I agree with Haxor, this is a sign you might need to buy a new one. I did after the controller that came with the Xbox One I purchased on Black Friday of 2015 began drifting. Depends on how much use it's gotten.
I've got a PDP Afterglow, getting on for a year old.

Has had very occasional glitches over its life and others have had more serious problems; the customer service is dubious.

But ... absolutely no drift and an app to adjust controller settings (including well featured audio) and underside, three position switches that i much prefer to paddles.
I did look at the Evil controllers but they're 5x the price of the PDP for similar functionality ...
I have had this with almost every controller I’ve gotten. The Xbox one controllers are made very cheaply. My advise is to get the extended warranty when you buy a new one. When one of my controllers starts to drift, I just take it to gamestop and they swap it out for a new one for no charge
Yep, time for a new controller if you don't want to deal with that. On the bright side, you'll be one controller closer to getting the CE achievement that needs 4 controllers to get if you haven't gotten it already.

You could try aftermarket controllers like Scuff for example, but they can be pricey.
i had the same issue. i was able to take it to a local gaming store and have a re build done they cleaned it took it all apart and the problem was fixed.