  We construct an extension of the MSSM in which superpartners can naturally be
heavier than the electroweak scale. This ``little hierarchy'' of scales is
stable because the Higgs arises as a pseudo-Nambu-Goldstone boson in the
breaking of an accidental SU(4) symmetry of the Higgs sector. Supersymmetry and
the global symmetry combine to forbid logarithmically divergent one-loop
contributions to the Higgs mass. The accidental symmetry follows from a simple
``twin'' parity which exchanges the SU(2) sectors in the SU(3)_C x SU(2)_L x
SU(2)_R x U(1)_X gauge group.
