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$\cdot$yr, characterized by an effective energy resolution of (7.7 $\pm$ 0.5) keV FWHM and a background in the region of interest of (0.014 $\pm$ 0.002) counts/(keV$\cdot$kg$\cdot$yr), we find no evidence for neutrinoless double-beta decay. The median statistical sensitivity of this search is $7.0\times10^{24}$ yr. Including systematic uncertainties, we place a lower limit on the decay half-life of $T^{0\nu}_{1/2}$($^{130}$Te) > $1.3\times 10^{25}$ yr (90% C.L.). Combining this result with those of two earlier experiments, Cuoricino and CUORE-0, we find $T^{0\nu}_{1/2}$($^{130}$Te) > $1.5\times 10^{25}$ 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 $m_{\beta\beta}<(110 - 520)$ meV, where the range reflects the nuclear matrix element estimates employed.

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...

First Results from CUORE: A Search for Lepton Number Violation via 0νββ Decay of Te130</mml:mrow...