© 2018 American Physical Society. 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-numberviolating process:130Te neutrinoless double-beta decay. Examining a total TeO2 exposure of 86.3 kg yr, characterized by an effective energy resolution of d7.7 ± 0.5T keV FWHM and a background in the region of interest of d0.014 ± 0.002T counts=dkeV kg yrT, we find no evidence for neutrinoless double-beta decay. Including systematic uncertainties, we place a lower limit on the decay half-life of T0ν1/2(130Te) > 1.3 × 1025yr (90% C.L.); the median statistical sensitivity of this search is 7.0 × 1024yr. Combining this result with those of two earlier experiments, Cuoricino and CUORE-0, we find T0ν1/2(130Te) > 1.5 × 1025yr (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 mββ< (110 - 520) meV, where the range reflects the nuclear matrix element estimates employed.