We report the results of a search for neutrinoless double-beta decay in a 9.8 kg⋅yr exposure of ¹³⁰Te 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 sensitivity of the experiment is 2.9 × 10²⁴ yr and surpasses the sensitivity of previous searches. We find no evidence for neutrinoless double-beta decay of ¹³⁰Te and place a Bayesian lower bound on the decay half-life, T_1∕2^0ν > 2.7 × 10²⁴ yr at 90% C.L. Combining CUORE-0 data with the the 19.75 kg⋅yr exposure of ¹³⁰Te from the Cuoricino experiment we obtain T_1∕2^0ν > 4.0 × 10²⁴ 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_ββ < 270–760 meV.