  We find evidence for the existence of solutions of the Einstein and Abelian
Higgs field equations describing a black hole pierced by a Nielsen-Olesen
vortex. This situation falls outside the scope of the usual no-hair arguments
due to the non-trivial topology of the vortex configuration and the special
properties of its energy-momentum tensor. By a combination of numerical and
perturbative techniques we conclude that the black hole horizon has no
difficulty in supporting the long range fields of the Nielsen Olesen string.
Moreover, the effect of the vortex can in principle be measured from infinity,
thus justifying its characterization as black hole ``hair".
