A Chern-Simons action for supergravity in odd-dimensional spacetimes is proposed. For all odd dimensions, the local symmetry group is a non trivial supersymmetric extension of the Poincar�� group. In $2+1$ dimensions the gauge group reduces to super-Poincar��, while for $D=5$ it is super-Poincar�� with a central charge. In general, the extension is obtained by the addition of a 1-form field which transforms as an antisymmetric fifth-rank tensor under Lorentz rotations. Since the Lagrangian is a Chern-Simons density for the supergroup, the supersymmetry algebra closes off shell without the need of auxiliary fields.

Revtex, 8 pages (two column format)