  The Dirac equation is solved in the Einstein-Yang-Mills background found by
Bartnik and McKinnon. We find a normalizable zero-energy fermion mode in the
$s$-wave sector. As shown recently, their solution corresponds to a
gravitational sphaleron which mediates transitions between topologically
distinct vacua. Since the Bartnik-McKinnon solution is unstable, it will either
collapse to form a black hole or radiate away its energy. In either case, as
the Chern-Simons number of the configuration changes, there will be an
accompanying anomalous change in fermion number.
