We report zero-field muon-spin rotation and relaxation measurements on the superconducting ferromagnet UCoGe. Weak itinerant ferromagnetic order is detected by a spontaneous muon-spin precession frequency below the Curie temperature TC=3 K. The micro+ precession frequency persists below the bulk superconducting transition temperature Tsc=0.5 K, where it measures a local magnetic field Bloc=0.015 T. The amplitude of the microSR signal provides unambiguous proof for ferromagnetism present in the whole sample volume. We conclude ferromagnetism coexists with superconductivity on the microscopic scale.