  Assuming the existence of a gauge boson $X$ which couples to $B - 3 L_\tau$,
we discuss the present experimental constraints on $g_X$ and $m_X$ from $Z \to
l^+ l^-$ and $Z \to \bar f f X~(f = q, \nu_\tau, \tau)$. We also discuss the
discovery potential of $X$ at hadron colliders through its decay into $\tau^+
\tau^-$ pairs. In the scenario where all three charged leptons (and their
neutrinos) mix, lepton flavor nonconservation through $X$ becomes possible and
provides another experimental probe into this hypothesis.
