The phase transition occurring at 25 K in NpO2, discovered almost 50 years ago, is the most long-lasting mystery in the physics of actinide compounds. Theories based on magnetic or electric-quadrupole order lead inevitably to fundamental, qualitative inconsistencies with observations. We show that the phenomenology of NpO2 can be understood if the order parameter is assumed to be a magnetic octupole of gamma(2) ( xyz) symmetry. NpO2 is the first compound for which indications of an octupolar phase transition have been found.