Chin augmentation would do nothing to improve your sleep apnea. The recessed chin is more than likely a result of an underdeveloped upper dental arch. The recessed lower jaw is also causing your tongue to be recessed into your airway which causes sleep apnea. Yes, a dental appliance can resolve your sleep apnea (depending on the severity of the diagnosis) and also correct your recessed chin. This can only be accomplished if you also enlarge your upper jaw. Enlarging your upper jaw and moving your lower jaw forward would require that you also wear braces to align your teeth. The dental appliance phase would take approximately nine months and the braces phase would require 12-18 months. This can also be accomplished surgically with an experienced surgeon. Good luck!