  A classification result for Ricci-flat anti-self-dual asymptotically locally
Euclidean 4-manifolds is obtained: they are either hyperk\"ahler (one of the
gravitational instantons classified by Kronheimer), or they are a cyclic
quotient of a Gibbons-Hawking space. The possible quotients are described in
terms of the monopole set in R^3, and it is proved that every such quotient is
actually K\"ahler. The fact that the Gibbons-Hawking spaces are the only
gravitational instantons to admit isometric quotients is proved by examining
the possible fundamental groups at infinity: most can be ruled out by the
classification of 3-dimensional spherical space form groups, and the rest are
excluded by a computation of the Rohklin invariant (in one case) or the eta
invariant (in the remaining family of cases) of the corresponding space forms.
