This paper compares several approximate methods for calculating rate coefficients for the O(P-3) + HCl reaction to presumably more accurate quantum mechanical calculations that an based on applying the J-shifting approximation (QM/JS) to an accurate cumulative reaction probability for J = O, All calculations for this work employ the recent S4 potential energy surface, which presents a number of challenges for the approximate methods. The O + HCl reaction also poses a significant challenge to computational dynamics because of the heavy-light-heavy mass combination and the broad noncollinear reaction path. The approximate methods for calculating the thermal rate coefficient that are examined in this article are quasiclassical trajectories (QCT), conventional transition state theory (TST), variational transition state theory employing the improved canonical variational theory (ICVT), ICVT with the microcanonical optimized multidimensional tunneling correction (ICVT/mu OMT), and reduced dimensionality quantum mechanical calculations based on adiabatic bend and J-shifting (QM/AB-JS) approximations. It is seen that QCT, TST, and ICVT rate coefficients agree with each other within a factor of 2.7 at 250 K and 1.6 at 1000 K, whereas inclusion of tunneling by the ICVT/mu OMT, QM/AB-JS, or QM/JS methods increases the late coefficients considerably. However, the ICVT/mu OMT and QM/AB-JS methods yield significantly lower rate coefficients than the QM/JS calculations, especially at lower temperatures. We also report and discuss calculations for the state-selected reaction of O(P-3) with HCl in the first excited vibrational state. In addition to the dynamics calculations, we report new electronic structure calculations by the Multi-Coefficient Gaussian-3 (MCG3) method that indicate that one possible source of disagreement between the QM/JS rate coefficients and experiment is that the barrier on the S4 surface may be too narrow.