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.
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Dr Young specializes in Facial Cosmetic and Reconstructive Surgery and is located in Bellevue near Seattle, Washington