We present results from the first phase of the KamLAND-Zen double-beta decay experiment, corresponding to an exposure of 89.5 kg yr of Xe-136. We obtain a lower limit for the neutrinoless double-beta decay half-life of T_{1/2}^{0{\nu}} > 1.9 x 10^{25} yr at 90% C.L. The combined results from KamLAND-Zen and EXO-200 give T_{1/2}^{0{\nu}} > 3.4 x 10^{25} yr at 90% C.L., which corresponds to a Majorana neutrino mass limit of < (120-250) meV based on a representative range of available matrix element calculations. Using those calculations, this result excludes the Majorana neutrino mass range expected from the neutrinoless double-beta decay detection claim in Ge-76, reported by a part of the Heidelberg-Moscow Collaboration, at more than 97.5% C.L