  We present a gauge model for the bimaximal mixing pattern among the neutrinos
that explains both the atmospheric and solar neutrino data via large angle
vacuum oscillation among the three known neutrinos. The model does not include
righthanded neutrinos but additional Higgs triplets which acquire naturally
small vev's due to the type II seesaw mechanism. A combination of global
$L_e-L_{\mu}-L_{\tau}$ and $S_3$ symmetries constrain the mass matrix for both
charged leptons and neutrinos in such a way that the bimaximal pattern emerges
naturally at the tree level and needed splittings among neutrinos at the one
loop level. This model predicts observable branching ratios for $\tau\to \mu
\mu\mu$, which could be used to test it.
