The Majorana Collaboration is operating an array of high purity Ge detectors to search for neutrinoless double-β decay in 76Ge. The Majorana Demonstrator comprises 44.1 kg of Ge detectors (29.7 kg enriched in 76Ge) split between two modules contained in a low background shield at the Sanford Underground Research Facility in Lead, South Dakota. Here we present results from data taken during construction, commissioning, and the start of full operations. We achieve unprecedented energy resolution of 2.5 keV FWHM at Qββ and a very low background with no observed candidate events in 9.95 kg yr of enriched Ge exposure, resulting in a lower limit on the half-life of 1.9×1025 yr(90% C.L.). This result constrains the effective Majorana neutrino mass to below 240–520 meV, depending on the matrix elements used. In our experimental configuration with the lowest background, the background is 4.0+3.1−2.5 counts/(FWHM t yr).