A precise measurement of the neutron decay β asymmetry A₀ has been carried out using polarized ultracold neutrons from the pulsed spallation ultracold neutron source at the Los Alamos Neutron Science Center. Combining data obtained in 2008 and 2009, we report A₀ = -0.119 66±0.000 89{-0.001 40}{+0.001 23}, from which we determine the ratio of the axial-vector to vector weak coupling of the nucleon g{A}/g{V}=-1.275 90{-0.004 45}{+0.004 09}.