  We consider the unique Hermitian connection with totally skew-symmetric
torsion on a Hermitian manifold. We prove that if the torsion is parallel and
the holonomy is Sp(n)U(1), considered as a subgroup of U(2n) x U(1), then the
manifold is locally isomorphic to the twistor space of a quaternionic Kaehler
manifold with positive scalar curvature. If the manifold is complete, then it
is globally isomorphic to such a twistor space.
