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 mπ ∼ 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 bs ∼ 0.123 fm, we find an H-dibaryon bound by B H ∞ = 16.6 ± 2.1 ± 4.6 MeV at a pion mass of mπ ∼ 389 MeV.It is now well established that quantum chromodynamics (QCD), the theory describing the dynamics of quarks and gluons, and the electroweak interactions, underlie all of nuclear physics, from the hadronic mass spectrum to the synthesis of heavy elements in stars. To date, there have been few quantitative connections between nuclear physics and QCD, but fortunately, Lattice QCD is entering an era in which precise predictions for hadronic quantities with quantifiable errors are being made. This development is particularly important for processes which are difficult to explore in the laboratory, such as hyperon-hyperon and hyperon-nucleon interactions for which knowledge is scarce, primarily due to the short lifetimes of the hyperons, but which may impact the late-stages of supernovae evolution. In this letter we report strong evidence for a bound H-dibaryon, a six-quark hadron with valence structure uuddss, from n f = 2 + 1 Lattice QCD calculations at light-quark masses that give the pion a mass of m π ∼ 389 MeV.The prediction of a relatively deeply bound system with the quantum numbers of ΛΛ (called the H-dibaryon) by Jaffe [1] in the late 1970s, based upon a bag-model calculation, started a vigorous search for such a system, both experimentally and also with alternate theoretical tools. Experimental constraints on, and phenomenological models of, the H-dibaryon can be found in Refs. [2,3,4]. While experimental studies of doublystrange hypernuclei restrict the H-dibaryon to be unbound or to have a small binding energy, the most recent constraints on the existence of the H-dibaryon come from heavy-ion collisions at RHIC, from which it is concluded that the H-dibaryon does not exist in the mass region 2.136 < M H < 2.231 GeV [5], effectively eliminating the possibility of a loosely-bound H-dibaryon at the physical light-quark masses. Recent experiments at KEK suggest there is a resonance near threshold in the H-dibaryon channel [6].The first study of baryon-baryon interactions with Lattice QCD was performed more than a decade ago [7,8]. This calculation was quenched and with m π > ∼ 550 MeV. The NPLQCD collaboration performed the first n f = 2+ 1 QCD calculations of baryon-baryon interactions [9,10] at low-energies but at unphysical pion masses. Quenched and dynamical calculations were subsequently performed by the HALQCD collaboration [11,12]. A number of quenched Lattice QCD calculations [13,14,15,16,17,18] have searched for the H-dibaryon, but to date no definitive results have been reported. Earlier work concluded that the H-dibaryon does not exi...