  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_pi ~ 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 ~ 0.123 fm, we find
an H-dibaryon bound by B = 16.6 +- 2.1 +- 4.6 MeV at a pion mass of m_pi ~ 389
MeV.
