  This paper proves the stability, with respect to the evolution determined by
the vacuum Einstein equations, of the Cartesian product of high-dimensional
Minkowski space with a compact, Ricci-flat Riemannian manifold that admits a
spin structure and a nonzero parallel spinor. Such a product includes the
example of Calabi-Yau and other special holonomy compactifications, which play
a central role in supergravity and string theory. The stability proved in this
paper provides a counter example to an instability argument by Penrose.
