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The spin-tunneling model of Hb--CO binding is used to calculate the binding rate at low temperature and high magnetic fields. The rate is calculated in second order perturbation theory assuming that spin-orbit coupling mediates the Hb iron electronic state change. The reaction which occurs at the crossing of the S = 2 and S = 0 energy vs. configuration coordinate curves is nonadiabatic, having a small electronic transition matrix element. Since detection of CO binding by polarized light in the Soret band makes it possible to observe hemes at specific orientation to the field direction, the rate is calculated for arbitrary heme orientation. Comparison with measurements at low temperature in zero field is made for spin quantization along the molecular crystal field direction.