The merger of two neutron stars has been predicted to produce an optical-infrared transient (lasting a few days) known as a 'kilonova', powered by the radioactive decay of neutron-rich species synthesized in the merger(1-5). Evidence that short gamma-ray bursts also arise from neutron-star mergers has been accumulating(6-8). In models(2,9) of such mergers, a small amount of mass (10(-4)-10(-2) solar masses) with a low electron fraction is ejected at high velocities (0.1-0.3 times light speed) or carried out by winds from an accretion disk formed around the newly merged object(10,11). This mass is expected to undergo rapid neutron capture (r-process) nucleosynthesis, leading to the formation of radioactive elements that release energy as they decay, powering an electromagnetic transient(1-3,9-14). A large uncertainty in the composition of the newly synthesized material leads to various expected colours, durations and luminosities for such transients(11-14). Observational evidence for kilonovae has so far been inconclusive because it was based on cases(15-19) of moderate excess emission detected in the afterglows of gamma-ray bursts. Here we report optical to near-infrared observations of a transient coincident with the detection of the gravitational-wave signature of a binary neutron-star merger and with a low-luminosity short-duration gamma-ray burst(20). Our observations, taken roughly every eight hours over a few days following the gravitational-wave trigger, reveal an initial blue excess, with fast optical fading and reddening. Using numerical models(21), we conclude that our data are broadly consistent with a light curve powered by a few hundredths of a solar mass of low-opacity material corresponding to lanthanide-poor (a fraction of 10(-4.5) by mass) ejecta.