I do these kind of repairs for a living. You'll most likely have to do a little solder work if you want it fixed properly. It's not terribly difficult to do of you've ever worked with solder. You'll want to go on ebay and order a "xbox one 3d analog module".
You'll need a torx security bit set with a T6 and T8. You should be able to find a set at an auto parts store or ifixit has a very nice tool kit for $25 that everyone should own. You'll need an iron, some solder and some solder wick.
You should be able to find a teardown guide which is pretty straightforward. Hold the wick against the solder joints with the iron to wick off the old solder, remove the old module, place the new one in and add solder to secure it in. It also helps to use flux to help work with the solder.
They demonstrate the solder process with this guide on a 360 controller. Same concept.
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