We report constraints on spin-independent weakly interacting massive particle (WIMP)-nucleon scattering using a 3.35×104 kg day exposure of the Large Underground Xenon (LUX) experiment. A dual-phase xenon time projection chamber with 250 kg of active mass is operated at the Sanford Underground Research Facility under Lead, South Dakota (USA). With roughly fourfold improvement in sensitivity for high WIMP masses relative to our previous results, this search yields no evidence of WIMP nuclear recoils. At a WIMP mass of 50 GeV c−2, WIMP-nucleon spin-independent cross sections above 2.2×10−46 cm2 are excluded at the 90% confidence level. When combined with the previously reported LUX exposure, this exclusion strengthens to 1.1×10−46 cm2 at 50 GeV c−2.