  We show that charged Eguchi-Hanson instantons provide a concrete and
calculable new source of intrinsic Peccei-Quinn symmetry breaking by quantum
gravity. The size of this breaking is shown to depend sensitively on the short
distance details of a given theory, but is generically suppressed by fermion
zero modes. Demanding that these gravitational effects not affet the axion
solution to the strong CP problem, we find that at least two sets of quarks
with differing Peccei-Quinn charges are required. In addition, these effects
obviate the cosmological axion domain wall problem but leave unchanged problems
associated with coherent axion oscillations.
