  E8 x E8 heterotic string and M-theory, when compactified on a Calabi-Yau
threefold admitting an SU(4) vector bundle with Wilson lines, can give rise to
the exact MSSM spectrum with three right-handed neutrino chiral superields, one
per family. Rank preserving Wilson lines require that the standard model group
be augmented by a gauged U(1)_B-L. Since there are no fields in this theory for
which 3(B-L) is an even, non-zero integer, the gauged B-L symmetry must be
spontaneously broken at a low scale, not too far above the electroweak scale.
It is shown that in these heterotic standard models, the B-L symmetry can be
broken, with a phenomenologically viable B-L/electroweak hierarchy, by at least
one right-handed sneutrino acquiring a vacuum expectation value. This is
explicitly demonstrated, in a specific region of parameter space, using a
renormalization group analysis and soft supersymmetry breaking operators. The
vacuum state is shown to be a stable, local minimum of the potential and the
resultant hierarchy is explicitly presented in terms of tan[beta].
