  Within the context of the E_8 x E_8 heterotic superstring compactified on a
smooth Calabi-Yau threefold with an SU(4) gauge instanton, we show the
existence of simple, realistic N=1 supersymmetric vacua that are compatible
with low energy particle physics. The observable sector of these vacua has
gauge group SU(3)_C x SU(2)_L x U(1)_Y x U(1)_{B-L}, three families of quarks
and leptons, each with an additional right-handed neutrino, two Higgs-Higgs
conjugate pairs, a small number of uncharged moduli and no exotic matter. The
hidden sector contains non-Abelian gauge fields and moduli. In the strong
coupling case there is no exotic matter, whereas for weak coupling there are a
small number of additional matter multiplets in the hidden sector. The
construction exploits a mechanism for ``splitting'' multiplets. The minimal
nature and rarity of these vacua suggest the possible theoretical and
experimental relevance of spontaneously broken U(1)_{B-L} gauge symmetry and
two Higgs-Higgs conjugate pairs. The U(1)_{B-L} symmetry helps to naturally
suppress the rate of nucleon decay.
