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 (136)Xe. We obtain a lower limit for the neutrinoless double-beta decay half-life of T(1/2)(0ν)>1.9×10(25) yr at 90% C.L. The combined results from KamLAND-Zen and EXO-200 give T(1/2)(0ν)>3.4×10(25) yr at 90% C.L., which corresponds to a Majorana neutrino mass limit of <m(ββ)> <(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 (76)Ge, reported by a part of the Heidelberg-Moscow Collaboration, at more than 97.5% C.L.