This is a Phase 2, prospective, randomized, double-masked, vehicle controlled, single-center study in approximately 12 subjects with LHON to evaluate safety, tolerability and efficacy of elamipretide (MTP-131) topical ophthalmic solution in this patient population. At the conclusion of 52 weeks of treatment, subjects will be offered the opportunity to enter an Open Label Extension for up to 48 additional weeks of treatment.