The origin of the unusual magnetism observed for crystalline CrPt3 films is investigated computationally, utilizing relativistic energy-band calculations. CrPt3 is found to belong to a novel class of ferromagnetic materials that are characterized by a violation of Hund's 3rd rule: a large orbital moment of 0.15μB develops on Cr parallel to the spin moment of 2.72μB. This anomalous property arrises from a profound Cr 3d–Pt 5d hybridization. Related to the unusual hybridization is the huge computed magnetocrystalline anisotropy energy of 0.55meV/unit cell, which is—understandably—larger than the room-temperature experimental value of 0.3meV/unit cell.