We report the results of a search for neutrinoless double-beta decay in a 9.8 kg yr exposure of $^{130}\mathrm{Te}$ using a bolometric detector array, CUORE-0. The characteristic detector energy resolution and background level in the region of interest are $5.1\ifmmode\pm\else\textpm\fi{}0.3\text{ }\text{ }\mathrm{keV}$ FWHM and $0.058\ifmmode\pm\else\textpm\fi{}0.004(\text{stat})\ifmmode\pm\else\textpm\fi{}\phantom{\rule{0ex}{0ex}}0.002(\text{syst})\mathrm{counts}/(\mathrm{keV}\text{ }\mathrm{kg}\text{ }\mathrm{yr})$, respectively. The median 90% C.L. lower-limit half-life sensitivity of the experiment is $2.9\ifmmode\times\else\texttimes\fi{}{10}^{24}\text{ }\text{ }\mathrm{yr}$ and surpasses the sensitivity of previous searches. We find no evidence for neutrinoless double-beta decay of $^{130}\mathrm{Te}$ and place a Bayesian lower bound on the decay half-life, ${T}_{1/2}^{0\ensuremath{\nu}}>2.7\ifmmode\times\else\texttimes\fi{}{10}^{24}\text{ }\text{ }\mathrm{yr}$ at 90% C.L. Combining CUORE-0 data with the 19.75 kg yr exposure of $^{130}\mathrm{Te}$ from the Cuoricino experiment we obtain ${T}_{1/2}^{0\ensuremath{\nu}}>4.0\ifmmode\times\else\texttimes\fi{}{10}^{24}\text{ }\text{ }\mathrm{yr}$ 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, ${m}_{\ensuremath{\beta}\ensuremath{\beta}}<270--760\text{ }\mathrm{meV}$.