We present experimental constraints on the spin-dependent WIMP-nucleon elastic cross sections from the total 129.5 kg-year exposure acquired by the Large Underground Xenon experiment ( LUX ) , operating at the Sanford Underground Research Facility in Lead , South Dakota ( USA ) . A profile likelihood ratio analysis allows 90 % CL upper limits to be set on the WIMP-neutron ( WIMP-proton ) cross section of \sigma _ { n } = 1.6 \times 10 ^ { -41 } cm ^ { 2 } ( \sigma _ { p } = 5 \times 10 ^ { -40 } cm ^ { 2 } ) at 35 GeV c ^ { -2 } , almost a sixfold improvement over the previous LUX spin-dependent results . The spin-dependent WIMP-neutron limit is the most sensitive constraint to date .