Braces Before or After Chin Surgery?

If you are simply adding to the surface of the chin (augmenting the profile etc), that shouldn't affect the bite.  In that case it doesn't matter and you can get started right away.
If the surgery affects the bite in any way, I would suggest waiting until after or simultaneously.

Chin implant surgery (or chin augmentation / chin enhancement / chin reduction / jaw implant surgery / chin silicone implant surgery / chin shaping / chin reshaping) occurs at the bottom of your chin and jaw area which are not in the same vicinity as your teeth and braces.
The only concern that I would have is regarding the hygiene in your oral cavity. With braces, you are more likely to have residue in your braces and around your teeth and the bacteria load is likely to be higher. Because of this I would rather do the approach through the bottom of your chin where the incision can hide really well. Otherwise, I think you can do it with having braces. Of course, I would wait until you are adjusted to any period where tightening of the braces occur for your comfort.

You chin procedure is called an advancement genioplasty. This is done by advancing the lower border of the mandible(lower jaw) and pogonion(chin), which has no affect on the teeth or your bite. As a result, this procedure can be done before or after braces. I would suggest seeing an orthodontist for evaluation.
I will tell you from experience that most of the time the chin is setback in relation to the upper jaw, the problem is the positioning of the lower jaw bone. This would require a bilateral sagittal split osteotomy (lower jaw advancement) to correct your chin position. If your chin point is also recessed, then the chin can also be done in combination with the lower jaw advancement. Advancing the chin where the underlying problem is really the lower jaw can have negative esthetic affects on your profile. Also, I would highly recommend seeing an oral maxillo-facial surgeon for evaluation. If you only need a chin advancement they will advance your bone rather than an implant which maybe used by a plastic surgeon. Your result will be much more pleasing and natural.
I have given you some big words which you can google to do you own research.