Single-pulse shock tube methods have been used to thermally generate hydrogen atoms and investigate the kinetics of their addition reactions with 1-butene at temperatures of 880 to 1120 K and pressures of 145 to 245 kPa. Rate parameters for the unimolecular decomposition of 1-butene are also reported. Addition of H atoms to the p bond of 1-butene results in displacement of either methyl or ethyl depending on whether addition occurs at the terminal or nonterminal position. Postshock monitoring of the initial alkene products has been used to determine the relative and absolute reaction rates. Absolute rate constants have been derived relative to the reference reaction of displacement of methyl from 1,3,5-trimethylbenzene (135TMB). With k(H + 135TMB -> m-xylene + CH3) = 6.7 x 10(13) exp(-3255/T) cm(3) mol(-1) s(-1), we find the following: k(H + 1-butene -> propene + CH3) = k(10) = 3.93 x 10(13) exp(-1152 K/T) cm(3) mol(-1) s(-1), [880-1120 K; 145-245 kPa]; k(H + 1-butene -> ethene + C2H5) = k(11) = 3.44 x 10(13) exp(-1971 K/T) cm(3) mol(-1) s(-1), [971-1120 K; 145-245 kPa]; k(10)/k(11) = 10((0.058 +/- 0.059)) exp [(818 +/- 141) K/T), 971-1120 K. Uncertainties (2 sigma) in the absolute rate constants are about a factor of 1.5, while the relative rate constants should be accurate to within +/- 15%. The displacement rate constants are shown to be very close to the high pressure limiting rate constants for addition of H, and the present measurements are the first direct determination of the branching ratio for 1-olefins at high temperatures. At 1000 K, addition to the terminal site is favored over the nonterminal position by a factor of 2.59 +/- 0.39, where the uncertainty is 2s and includes possible systematic errors. Combining the present results with evaluated data from the literature pertaining to temperatures of <440 K leads us to recommend the following: k(infinity)(H + 1-butene -> 2-butyl) = 1.05 x 10(9)T(1.40) exp(-366/T) cm(3) mol(-1) s(-1), [220-2000 K]; k(infinity)(H + 1-butene -> 1-butyl) = 9.02 x 10(8)T(1.40) exp(-1162/T) cm(3) mol(-1) s(-1) [220-2000 K]. Analogous rate constants for other unbranched 1-olefins should be very similar. Despite this, a factor of three discrepancy in the branching ratio for terminal and nonterminal addition is noted when comparing the present values with recommendations from a recent model of the important H + propene reaction. This difference is suggested to be well outside of the possible experimental errors of the present study or the expected differences with 1-butene. There thus appear to be inconsistencies in the current model for propene. In particular the addition branching ratio from that model should not be used as a reference value in extrapolations to other systems via rate rules or automated mechanism generation techniques.