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We report the discovery and monitoring of the near-infrared counterpart (AT2017gfo) of a binary neutron-star merger event detected as a gravitational wave source by Advanced Laser Interferometer Gravitational-wave Observatory (LIGO)/Virgo (GW170817) and as a short gamma-ray burst by Fermi Gamma-ray Burst Monitor (GBM) and Integral SPI-ACS (GRB 170817A). The evolution of the transient light is consistent with predictions for the behavior of a "kilonova/macronova" powered by the radioactive decay of massive neutron-rich nuclides created via r-process nucleosynthesis in the neutron-star ejecta. In particular, evidence for this scenario is found from broad features seen in Hubble Space Telescope infrared spectroscopy, similar to those predicted for lanthanide-dominated ejecta, and the much slower evolution in the near-infrared K s -band compared to the optical. This indicates that the late-time light is dominated by high-opacity lanthanide-rich ejecta, suggesting nucleosynthesis to the third r-process peak (atomic masses A 195 ). This discovery confirms that neutron-star mergers produce kilo-/macronovae and that they are at least a major-if not the dominant-site of rapid neutron capture nucleosynthesis in the universe.