We present evidence for the existence of a bound H dibaryon, an I=0, J=0, s=-2 state with valence quark structure uuddss, at a pion mass of m(π)∼389 MeV. Using the results of lattice QCD calculations performed on four ensembles of anisotropic clover gauge-field configurations, with spatial extents of L∼2.0, 2.5, 3.0, and 3.9 fm at a spatial lattice spacing of b(s)∼0.123 fm, we find an H dibaryon bound by B(∞)(H)=16.6±2.1±4.6 MeV at a pion mass of m(π)∼389 MeV.