  If the minimal standard model of quarks and leptons is extended to include
just a righthanded partner to nu_tau, then the quantum number B-3L_tau can be
added as a gauge symmetry without the appearance of anomalies. A suitable
extension of the scalar sector allows one neutrino to have a seesaw mass, and
the other two to have radiative masses, with acceptable phenomenological values
for neutrino oscillations. The B-3L_tau gauge boson may be light and be
observable through its decay into tau^+ tau^-.
