Within the context of the E8×E8 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×SU(2)L×U(1)Y×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