We present ground-based optical and Hubble Space Telescope optical and near-IR observations of the short-hard GRB 130603B at z = 0.356 , which demonstrate the presence of excess near-IR emission matching the expected brightness and color of an r-process powered transient ( a “ kilonova ” ) . The early afterglow fades rapidly with \alpha \lesssim - 2.6 at t \approx 8 - 32 hr post-burst and has a spectral index of \beta \approx - 1.5 ( F _ { \nu } \propto t ^ { \alpha } \nu ^ { \beta } ) , leading to an expected near-IR brightness at the time of the first HST observation of m _ { F 160 W } ( { t = 9.4 d } ) \gtrsim 29.3 AB mag . Instead , the detected source has m _ { F 160 W } = 25.8 \pm 0.2 AB mag , corresponding to a rest-frame absolute magnitude of M _ { J } \approx - 15.2 mag . The upper limit in the HST optical observations is m _ { F 606 W } \gtrsim 27.7 AB mag ( 3 \sigma ) , indicating an unusually red color of V - H \gtrsim 1.9 mag . Comparing the observed near-IR luminosity to theoretical models of kilonovae produced by ejecta from the merger of an NS-NS or NS-BH binary , we infer an ejecta mass of M _ { ej } \approx 0.03 - 0.08 M _ { \odot } for v _ { ej } \approx 0.1 - 0.3 c . The inferred mass matches the expectations from numerical merger simulations . The presence of a kilonova provides the strongest evidence to date that short GRBs are produced by compact object mergers , and provides initial insight on the ejected mass and the primary role that compact object merger may play in the r-process . Equally important , it demonstrates that gravitational wave sources detected by Advanced LIGO/Virgo will be accompanied by optical/near-IR counterparts with unusually red colors , detectable by existing and upcoming large wide-field facilities ( e.g. , Pan-STARRS , DECam , Subaru , LSST ) .