We report on a high-statistics measurement of the deuteron spin structure function g[sup d][sub 1] at a beam energy of 29 GeV in the kinematic range 0.029 < x < 0.8 and 1 < Q2 < 10 (GeV/c)2. The integral Gamma [sup d][sub 1] = (integral)[sup 1][sub 0]g[sup d][sub 1]dx evaluated at fixed Q2 = 3 (GeV/c)2 gives 0.042 ± 0.003(stat) ± 0.004(syst). Combining this result with our earlier measurement of g[sup p][sub 1], we find Gamma [sup p][sub 1]- Gamma [sup n][sub 1] = 0.163 ± 0.010(stat) ± 0.016(syst), which agrees with the prediction of the Bjorken sum rule with O( alpha [sup 3][sub s]) corrections, Gamma [sup p][sub 1]- Gamma [sup n][sub 1] = 0.171 ± 0.008. We find the quark contribution to the proton helicity to be Delta q = 0.30 ± 0.06
