  We give an alternative description of the Schoen manifold as the blow-up of a
Z2xZ2 orbifold in which one Z2 factor acts as a roto-translation. Since for
this orbifold the fixed tori are only identified in pairs but not orbifolded,
four-dimensional chirality can never be obtained in heterotic string
compactifications using standard techniques alone. However, chirality is
recovered when its tori become magnetized. To exemplify this, we construct an
E8xE8' heterotic SU(5) GUT on the Schoen manifold with Abelian gauge fluxes,
which becomes an MSSM with three generations after an appropriate Wilson line
is associated to its freely acting involution. We reproduce this model as a
standard heterotic orbifold CFT of the (partially) blown down Schoen manifold
with a magnetic flux. Finally, in analogy to a proposal for non--perturbative
heterotic models by Aldazabal et al. we suggest modifications to the heterotic
orbifold spectrum formulae in the presence of magnetized tori.
