  We analyze the production of multileptons in the simplest supergravity model
with bilinear violation of R parity at the Fermilab Tevatron. Despite the small
R-parity violating couplings needed to generate the neutrino masses indicated
by current atmospheric neutrino data, the lightest supersymmetric particle is
unstable and can decay inside the detector. This leads to a phenomenology quite
distinct from that of the R-parity conserving scenario. We quantify by how much
the supersymmetric multilepton signals differ from the R-parity conserving
expectations, displaying our results in the $m_0 \otimes m_{1/2}$ plane. We
show that the presence of bilinear R-parity violating interactions enhances the
supersymmetric multilepton signals over most of the parameter space, specially
at moderate and large $m_0$.
