OH and OD product branching ratios and internal state distributions have been measured in a state-to-state study of the reaction H+HOD(nu1,nu2,nu3)-->OH(v,N)(OD(v,N))+HD(H2). The HOD molecules are prepared in a specific vibrational level (one or two J states) by infrared excitation of thermal HOD using a tunable optical parametric oscillator. Fast (''hot'') H atoms are generated by laser photolysis of HI at 266 nm, and the OH and OD reaction products are probed quantum-state-specifically by laser-induced fluorescence. The OD:OH product branching ratios demonstrate that we achieve bond-specific chemistry at the lowest possible level of vibrational excitation for the H + HOD reaction: excitation of either bond with one quantum of vibration leads to selective cleavage of that bond. The OD:OH ratio is 1.38 +/- 0. 14 for the reaction H + HOD(0,0,0) (ground-state HOD). In contrast, this ratio is greater than 25:1 for H + HOD(0,0,1) and less than 1:5.8 for H + HOD(1,0,0) (i.e.,OH:OD > 5.8:1). Here (0,0,1) and (1,0,0) denote the O-Hand O-D stretch fundamentals, respectively. We find that excitation of these stretching vibrations increases the reaction cross section by a factor of as much as 120 over the increase resulting from an equivalent amount of extra translational energy, which is the behavior expected for a reaction with a late barrier. These results can also be understood in terms of a simple geometric model of the reaction, wherein vibrational excitation widens the cone of acceptance for reaction. The reaction H + HOD(1,0,0) produces a small amount of OD(v=1), which is approximately 5% of the amount of OH(v=0) produced. No vibrationally excited OH or OD was observed in the reactions with HOD(0,0,1) or HOD(0,0,0). OH and OD product rotational and electronic fine-structure distributions were also measured, as were the product state distributions for the reactions H + H2O and H + D2O (for comparison to the title reaction). All rotational distributions are well described by temperatures( i.e., Boltzmann distributions); OD products are consistently hotter than OH products (930 K vs 660 K). This observation suggests that rotational ''citation of the hydroxyl product occurs mainly through impulsive energy release in the breaking of the OH or OD bond. The PI(A')/PI(A'') LAMBDA-doublet ratio is greater than 4 in the high-J limit, which also supports this impulsive model. All of these results support the well-established picture that the nonreacting OH or OD bond acts as a ''spectator'' in this reaction.