The heterotic standard embedding on a Calabi-Yau threefold yields an E_6 grand unified theory in four dimensions. The gauge symmetry can be partially broken by turning on discrete Wilson lines, but such models necessarily feature an extended gauge group and exotic light matter fields. I will describe the recent construction of compactifications on a new three-generation manifold which solve both these problems via supersymmetric deformations of the gauge bundle. Such deformations can be interpreted as the supersymmetric Higgs mechanism in four dimensions, but our top-down construction allows us to keep control of the theory, and perform a reliable computation of the resulting spectrum. The moduli space breaks up into a number of branches depending on the initial choice of Wilson lines, and on eight of these branches we find models whose light charged spectrum is exactly that of the minimal supersymmetric standard model: unbroken gauge group SU(3)xSU(2)xU(1), three generations of quarks and leptons, and one pair of Higgs doublets.