  We show that in certain compactifications of ${\cal M}$-theory on
eight-manifolds to three-dimensional Minkowski space-time the four-form field
strength can have a non-vanishing expectation value, while an $N=2$
supersymmetry is preserved. For these compactifications a warp factor for the
metric has to be taken into account. This warp factor is non-trivial in three
space-time dimensions due to Chern-Simons corrections to the fivebrane Bianchi
identity. While the original metric on the internal space is not K\"ahler, it
can be conformally transformed to a metric that is K\"ahler and Ricci flat, so
that the internal manifold has $SU(4)$ holonomy.
