We report on the fabrication and characterization of magnetic tunnel junctions consisting of a single layer of graphene as the tunnel barrier, sandwiched between two metallic ferromagnetic electrodes. We employ a fabrication process chosen to minimize oxidation of the electrode materials at the ferromagnet/graphene interfaces. The devices have low resistance-area products of 1.5-6 m2, with low-temperature magnetoresistances of 1.5-3.4%. The temperature and bias dependencies of the resistance confirm that transport is dominated by tunneling processes rather than by any unintended pinholes. © 2014 American Physical Society.