  A finite action principle for three-dimensional gravity with negative
cosmological constant, based on a boundary condition for the asymptotic
extrinsic curvature, is considered. The bulk action appears naturally
supplemented by a boundary term that is one half the Gibbons-Hawking term, that
makes the Euclidean action and the Noether charges finite without additional
Dirichlet counterterms. The consistency of this boundary condition with the
Dirichlet problem in AdS gravity and the Chern-Simons formulation in three
dimensions, and its suitability for the higher odd-dimensional case, are also
discussed.
