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We report the results of a search for neutrinoless double-beta decay in a 9.8 kg yr exposure of Te-130 using a bolometric detector array, CUORE-0. The characteristic detector energy resolution and background level in the region of interest are 5.1 +/- 0.3 keV FWHM and 0.058 +/- 0.004(stat) +/- 0.002(syst)counts/(keV kg yr), respectively. The median 90% C.L. lower-limit half-life sensitivity of the experiment is 2.9 x 10(24) yr and surpasses the sensitivity of previous searches. We find no evidence for neutrinoless double-beta decay of Te-130 and place a Bayesian lower bound on the decay half-life, T-1/2(0 nu) > 2.7 x 10(24) yr at 90% C.L. Combining CUORE-0 data with the 19.75 kg yr exposure of Te-130 from the Cuoricino experiment we obtain T-1/2(0 nu) > 4.0 x 10(24) yr at 90% C.L. (Bayesian), the most stringent limit to date on this half-life. Using a range of nuclear matrix element estimates we interpret this as a limit on the effective Majorana neutrino mass, m beta beta < 270-760 meV.