Gamma-ray bursts (GRBs) divide into two classes: 'long', which typically have initial durations of T90 > 2 s, and 'short', with durations of T90 < 2 s (where T90 is the time to detect 90% of the observed fluence). Long bursts, which on average have softer gamma-ray spectra, are known to be associated with stellar core-collapse events-in some cases simultaneously producing powerful type Ic supernovae. In contrast, the origin of short bursts has remained mysterious until recently. A subsecond intense 'spike' of gamma-rays during a giant flare from the Galactic soft gamma-ray repeater, SGR 1806-20, reopened an old debate over whether some short GRBs could be similar events seen in galaxies out to approximately 70 Mpc (refs 6-10; redshift z approximately 0.016). Shortly after that, localizations of a few short GRBs (with optical afterglows detected in two cases) have shown an apparent association with a variety of host galaxies at moderate redshifts. Here we report a correlation between the locations of previously observed short bursts and the positions of galaxies in the local Universe, indicating that between 10 and 25 per cent of short GRBs originate at low redshifts (z < 0.025).