The statistical phase-space theory of Light, Pechukas, and Nikitin is applied to the endothermic reaction K+HCl→KCl+H. The results are compared to molecular beam experiments. The probability of reaction as a function of impact parameter is in fair agreement with that obtained by Moursund et al., but the phase-space theory predicts too high a reaction cross section. Further, the calculations suggest that their determination of the maximum impact parameter leading to each excited vibrational state of the product should not be trusted. The phase-space calculations, combined with an estimate of rotationally inelastic grazing collisions, predict a high ratio (2-10) of rotationally inelastic collisions to reactive collisions; the effect of these nonreactive collisions on the optical model analysis of reactive scattering is not known. Because we assumed threshold for reaction of less than 1 kcal/mole, our results are not quantitatively comparable to those of Odiorne and Brooks. Nevertheless our full calculations are in essential agreement with the ideas about angular momentum disposal which Moursund et al. and Odiorne and Brooks used to provide interpretations of their data. Many detailed properties of the reactions are predicted; these can be compared with future beam experiments. The direction and magnitude of the quantitative deviation from the experimental results is a useful guide to understanding the chemical dynamics of this collision system since the statistical phase-space theory indicates what the results would be in the limiting case that all degrees of freedom of the interacting system are coupled in the most efficient possible way.