  A fake projective plane is a compact complex manifold of dimension 2 which
has the same Betti numbers as the complex projective plane, but not isomorphic
to the complex projective plane. As was shown by D. Mumford, there exists at
least one such surface.
  In this paper we prove the existence of a fake projective plane which is
birational to a cyclic cover of degree 7 of a Dolgachev surface.
