  We present a locally supersymmetric extension of the minimal supersymmetric
Standard Model (MSSM) based on the gauge group $SU(3)_C\times SU(2)_L\times
U(1)_Y\times U(1)^\prime$ where, except for the supersymmetry breaking scale
which is fixed to be $\sim 10^{11}$ GeV, we require that all non-Standard-Model
parameters allowed by the {\it local} spacetime and gauge symmetries assume
their natural values. The $U(1)^\prime$ symmetry, which is spontaneously broken
at the intermediate scale, serves to ({\it i}) explain the weak scale
magnitudes of $\mu$ and $b_\mu$ terms, ({\it ii}) ensure that dimension-3 and
dimension-4 baryon-number-violating superpotential operators are forbidden,
solving the proton-lifetime problem, ({\it iii}) predict {\it bilinear lepton
number violation} in the superpotential at just the right level to accommodate
the observed mass and mixing pattern of active neutrinos (leading to a novel
connection between the SUSY breaking scale and neutrino masses), while
corresponding trilinear operators are strongly supppressed. The phenomenology
is like that of the MSSM with bilinear R-parity violation, were the would-be
lightest supersymmetric particle decays leptonically with a lifetime of $\sim
10^{-12}-10^{-8}$ s. Theoretical consistency of our model requires the
existence of multi-TeV, stable, colour-triplet, weak-isosinglet scalars or
fermions, with either conventional or exotic electric charge which should be
readily detectable if they are within the kinematic reach of a hadron collider.
Null results of searches for heavy exotic isotopes implies that the re-heating
temperature of our Universe must have been below their mass scale which, in
turn, suggests that sphalerons play a key role for baryogensis. Finally, the
dark matter cannot be the weakly interacting neutralino.
