  We construct supersymmetric compactifications of E_8 \times E_8 heterotic
string theory which realise exactly the massless spectrum of the Minimal
Supersymmetric Standard Model (MSSM) at low energies. The starting point is the
standard embedding on a Calabi-Yau threefold which has Hodge numbers
(h^11,h^21) = (1,4) and fundamental group Z_12, which gives an E_6 grand
unified theory with three net chiral generations. The gauge symmetry is then
broken to that of the standard model by a combination of discrete Wilson lines
and continuous deformation of the gauge bundle. On eight distinct branches of
the moduli space, we find stable bundles with appropriate cohomology groups to
give exactly the massless spectrum of the MSSM.
