  We construct a supersymmetric SU(2)_L X SU(2)_R X U(1)_B-L model in which a
discrete symmetry (C-parity) implements strict left-right symmetry in the
scalar (Higgs) sector. Although two electroweak bidoublets are introduced to
accommodate the observed fermion masses and mixings, a natural missing partner
mechanism insures that a single pair of MSSM Higgs doublets survives below the
left-right symmetry breaking scale. If this scale happens to lie in the TeV
range, several new particles potentially much lighter than the SU(2)_R charged
gauge bosons W_R^+- will be accessible at the LHC.
