  Despite a rich phenomenology, gamma-ray bursts (GRBs) are divided into two
classes based on their duration and spectral hardness -- the long-soft and the
short-hard bursts. The discovery of afterglow emission from long GRBs was a
watershed event, pinpointing their origin to star forming galaxies, and hence
the death of massive stars, and indicating an energy release of about 10^51
erg. While theoretical arguments suggest that short GRBs are produced in the
coalescence of binary compact objects (neutron stars or black holes), the
progenitors, energetics, and environments of these events remain elusive
despite recent localizations. Here we report the discovery of the first radio
afterglow from a short burst, GRB 050724, which unambiguously associates it
with an elliptical galaxy at a redshift, z=0.257. We show that the burst is
powered by the same relativistic fireball mechanism as long GRBs, with the
ejecta possibly collimated in jets, but that the total energy release is
10-1000 times smaller. More importantly, the nature of the host galaxy
demonstrates that short GRBs arise from an old (>1 Gyr) stellar population,
strengthening earlier suggestions, and providing support for coalescing compact
object binaries as the progenitors.
