Here we show, with simultaneous transport and photoemission measurements, that the graphene-terminated SiC(0001) surface undergoes a metal-insulator transition upon dosing with small amounts of atomic hydrogen. We find the room temperature resistance increases by about 4 orders of magnitude, a transition accompanied by anomalies in the momentum-resolved spectral function including a non-Fermi-liquid behavior and a breakdown of the quasiparticle picture. These effects are discussed in terms of a possible transition to a strongly (Anderson) localized ground state.