  A static wormhole solution for gravity in vacuum is found for odd dimensions
greater than four. In five dimensions the gravitational theory considered is
described by the Einstein-Gauss-Bonnet action where the coupling of the
quadratic term is fixed in terms of the cosmological constant. In higher
dimensions d=2n+1, the theory corresponds to a particular case of the Lovelock
action containing higher powers of the curvature, so that in general, it can be
written as a Chern-Simons form for the AdS group. The wormhole connects two
asymptotically locally AdS spacetimes each with a geometry at the boundary
locally given by R times S^{1} times H_{d-3}. Gravity pulls towards a fixed
hypersurface located at some arbitrary proper distance parallel to the neck.
The causal structure shows that both asymptotic regions are connected by light
signals in a finite time. The Euclidean continuation of the wormhole is smooth
independently of the Euclidean time period, and it can be seen as instanton
with vanishing Euclidean action. The mass can also be obtained from a surface
integral and it is shown to vanish.
