  It is shown that strongly coupled heterotic M-theory with anti-five-branes in
the S^1/Z_2 bulk space can have meta-stable vacua which break N=1 supersymmetry
and have a small, positive cosmological constant. This is demonstrated for the
"minimal" heterotic standard model. This vacuum has the exact MSSM matter
spectrum in the observable sector, a trivial hidden sector vector bundle and
both five-branes and anti-five-branes in the bulk space. The Kahler moduli for
which the cosmological constant has phenomenologically acceptable values are
shown to also render the observable sector vector bundle slope-stable. A
corollary of this result is that strongly coupled M-theory vacua with only
five-branes in the S^1/Z_2 interval may have stabilized moduli, but at a
supersymmetry preserving minimum with a large, negative cosmological constant.
