  We construct static black hole solutions that have no rotational symmetry.
These arise in theories, including the standard electroweak model, that include
charged vector mesons with mass $m\ne 0$. In such theories, a magnetically
charged Reissner-Nordstrom black hole with horizon radius less than a critical
value of the order of $m^{-1}$ is classically unstable against the development
of a nonzero vector meson field just outside the horizon, indicating the
existence of static black hole solutions with vector meson hair. For the case
of unit magnetic charge, spherically symmetric solutions of this type have
previously been studied. For other values of the magnetic charge, general
arguments show that any new solution with hair cannot be spherically symmetric.
In this paper we develop and apply a perturbative scheme (which may have
applicability in other contexts) for constructing such solutions in the case
where the Reissner-Nordstrom solution is just barely unstable. For a few low
values of the magnetic charge the black holes retain a rotational symmetry
about a single axis, but this axial symmetry disappears for higher charges.
While the vector meson fields vanish exponentially fast at distances greater
than $O(m^{-1})$, the magnetic field and the metric have higher multipole
components that decrease only as powers of the distance from the black hole.
