The Large Underground Xenon (LUX) collaboration has designed and constructed a dual-phase xenon detector, in order to conduct a search for Weakly Interacting Massive Particles(WIMPs), a leading dark matter candidate. The goal of the LUX detector is to clearly detect (or exclude) WIMPS with a spin independent cross section per nucleon of $2times 10^{-46}$ cm$^{2}$, equivalent to $sim$1 event/100 kg/month in the inner 100-kg fiducial volume (FV) of the 370-kg detector. The overall background goals are set to have $<$1 background events characterized as possible WIMPs in the FV in 300 days of running. This paper describes the design and construction of the LUX detector.