Edge supercurrents in superconductors have long been an elusive target. Interest in them has reappeared in the context of topological superconductivity. We report evidence for the existence of a robust edge supercurrent in the Weyl superconductor molybdenum ditelluride (MoTe2). In a magnetic field B, fluxoid quantization generates a periodic modulation of the edge condensate observable as a "fast-mode" oscillation of the critical current l c versus B. The fast-mode frequency is distinct from the conventional Fraunhofer oscillation displayed by the bulk supercurrent. We confirm that the fast-mode frequency increases with crystal area as expected for an edge supercurrent. In addition, weak excitation branches are resolved that display an unusual broken symmetry.