The Large Underground Xenon (LUX) experiment is a dual-phase xenon time-projection chamber operating at the Sanford Underground Research Facility (Lead, South Dakota). The LUX cryostat was filled for the first time in the underground laboratory in February 2013. We report results of the first WIMP search data set, taken during the period from April to August 2013, presenting the analysis of 85.3 live days of data with a fiducial volume of 118 kg. A profile-likelihood analysis technique shows our data to be consistent with the background-only hypothesis, allowing 90% confidence limits to be set on spin-independent WIMP-nucleon elastic scattering with a minimum upper limit on the cross section of 7.6×10−46 cm2 at a WIMP mass of 33 GeV/c2. We find that the LUX data are in disagreement with low-mass WIMP signal interpretations of the results from several recent direct detection experiments.