  Evidence for $\bar \nu_{\mu} \rightarrow \bar \nu_e$ oscillations has been
reported at LAMPF using the LSND detector. Further evidence for neutrino mixing
comes from the solar neutrino deficit and the atmospheric neutrino anomaly. All
of these anomalies require new physics. We show that all of these anomalies can
be explained if the standard model is enlarged so that an unbroken parity
symmetry can be defined. This explanation holds independently of the actual
model for neutrino masses. Thus, we argue that parity symmetry is not only a
beautiful candidate for a symmetry beyond the standard model, but it can also
explain the known neutrino physics anomalies.
