  We construct a left-right symmetric model based on the gauge group
$SU(2)_L\times SU(2)_R\times U(1)_{B-L}$ in five dimensions where both the
gauge bosons and fermions reside in all five dimensions. The orbifold boundary
conditions are used not only to break the gauge symmetry down to $SU(2)_L\times
U(1)_Y\times U(1)_{Y'}$ but also to ``project'' the right handed neutrino out
of the zero mode part of the spectrum, providing a new way to understand the
small neutrino masses without adding (singlet) bulk neutrinos. This formulation
of the left-right model has also two new features: (i) it avoids most existing
phenomenological bounds on the scale of the right handed $W_R$ boson allowing
for the possibility that the right handed gauge bosons could have masses under
a TeV, and (ii) it predicts a stable lepton with mass of order of the inverse
radius of the fifth dimension.
