First Results from CUORE: A Search for Lepton Number Violation via <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mn>0</mml:mn><mml:mi>ν</mml:mi><mml:mi>β</mml:mi><mml:mi>β</mml:mi></mml:mrow></mml:math> Decay of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mmultiscripts><mml:mrow><mml:mi>Te</mml:mi></mml:mrow><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>130</mml:mn></mml:mrow></mml:mmultiscripts></mml:mrow></mml:math>

The CUORE experiment, a ton-scale cryogenic bolometer array, recently began operation at the Laboratori Nazionali del Gran Sasso in Italy. The array represents a significant advancement in this technology, and in this work we apply it for the first time to a high-sensitivity search for a lepton-number-violating process: ^{130}Te neutrinoless double-beta decay. Examining a total TeO_{2} exposure of 86.3 kg yr, characterized by an effective energy resolution of (7.7±0.5) keV FWHM and a background in the region of interest of (0.014±0.002) counts/(keV kg yr), we find no evidence for neutrinoless double-beta decay. Including systematic uncertainties, we place a lower limit on the decay half-life of T_{1/2}^{0ν}(^{130}Te)>1.3×10^{25} yr (90% C.L.); the median statistical sensitivity of this search is 7.0×10^{24} yr. Combining this result with those of two earlier experiments, Cuoricino and CUORE-0, we find T_{1/2}^{0ν}(^{130}Te)>1.5×10^{25} yr (90% C.L.), which is the most stringent limit to date on this decay. Interpreting this result as a limit on the effective Majorana neutrino mass, we find m_{ββ}<(110-520) meV, where the range reflects the nuclear matrix element estimates employed.