We show that dark photons (A ) with masses ∼ 10-80 MeV can be probed in the decay µ + → e + ν eνµ A , A → e + e − , with the upcoming Mu3e experiment at the Paul Scherrer Institute (PSI) in Switzerland. With an expected 10 15 (5.5 × 10 16 ) muon decays in 2015-2016 (2018 and beyond), Mu3e has the exciting opportunity to probe a substantial fraction of currently unexplored dark photon parameter space, probing kineticmixing parameter, , as low as 2 ∼ 10 −7 (10 −8 ). No modifications of the existing Mu3e setup are required.