Ab initio molecular orbital theory has been used to calculate the exchange barriers for the reaction H + XH. The calculations employed large basis sets, and a variety of methods were used to calculate the correlation energy up through PMP4 and QCISD(T) (or CCSD(T)). The barriers to exchange at the QCISD(T) level, uncorrected for zero point effects, are 42.7, 20.2, 13.8, and 6.4 kcal/mol for X = F, Cl, Br, and 1, respectively. The effect of basis set superposition was studied and found to be 0.4-2.2 kcal/mol depending on X and the basis set. These barriers are consistent with previous calculations which show large barriers instead of the low barriers expected from a number of experimental results. Rate constants and effective activation energies were calculated from transition-state theory and compared to experiment. The results suggest that the experiments need to be reinterpreted in terms of large activation energies instead of the small values used in many of the previous studies.