  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\'e group. In $2+1$ dimensions the gauge
group reduces to super-Poincar\'e, while for $D=5$ it is super-Poincar\'e 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.
