  Gravitational waves were discovered with the detection of binary black hole
mergers and they should also be detectable from lower mass neutron star
mergers. These are predicted to eject material rich in heavy radioactive
isotopes that can power an electromagnetic signal called a kilonova. The
gravitational wave source GW170817 arose from a binary neutron star merger in
the nearby Universe with a relatively well confined sky position and distance
estimate. Here we report observations and physical modelling of a rapidly
fading electromagnetic transient in the galaxy NGC4993, which is spatially
coincident with GW170817 and a weak short gamma-ray burst. The transient has
physical parameters broadly matching the theoretical predictions of blue
kilonovae from neutron star mergers. The emitted electromagnetic radiation can
be explained with an ejected mass of 0.04 +/- 0.01 Msol, with an opacity of
kappa <= 0.5 cm2/gm at a velocity of 0.2 +/- 0.1c. The power source is
constrained to have a power law slope of beta = -1.2 +/- 0.3, consistent with
radioactive powering from r-process nuclides. We identify line features in the
spectra that are consistent with light r-process elements (90 < A < 140). As it
fades, the transient rapidly becomes red, and emission may have contribution by
a higher opacity, lanthanide-rich ejecta component. This indicates that neutron
star mergers produce gravitational waves, radioactively powered kilonovae, and
are a nucleosynthetic source of the r-process elements.
