It has long been known that there are two classes of gamma-ray bursts (GRBs), mainly distinguished by their durations. The breakthrough in our understanding of long-duration GRBs (those lasting more than approximately 2 s), which ultimately linked them with energetic type Ic supernovae, came from the discovery of their long-lived X-ray and optical 'afterglows', when precise and rapid localizations of the sources could finally be obtained. X-ray localizations have recently become available for short (duration <2 s) GRBs, which have evaded optical detection for more than 30 years. Here we report the first discovery of transient optical emission (R-band magnitude approximately 23) associated with a short burst: GRB 050709. The optical afterglow was localized with subarcsecond accuracy, and lies in the outskirts of a blue dwarf galaxy. The optical and X-ray afterglow properties 34 h after the GRB are reminiscent of the afterglows of long GRBs, which are attributable to synchrotron emission from ultrarelativistic ejecta. We did not, however, detect a supernova, as found in most nearby long GRB afterglows, which suggests a different origin for the short GRBs.