The methoxy radical undergoes the dynamic Jahn-Teller effect which gives rise to diagonal and off-diagonal hyperfine coupling constants. The off-diagonal constants are between the degenerate vibronic wave functions of the lowest spin-orbit level, The experimental hyperfine coupling constants were measured in terms of spherical tensors. In this paper the spherical tensors are expanded in Cartesian matrix elements. These expansions are used to calculate the hyperfine coupling constants, both the isotropic constants (also known as the Fermi contact terms) and the anisotropic constants (also known as the dipolar terms). The diagonal hyperfine coupling constants could be calculated by standard methods, but the off-diagonal hyperfine coupling constants had to be calculated between nonorthogonal orbitals. The calculated dipolar hyperfine terms, both diagonal and off-diagonal, are in fair agreement with the known experimental values. The calculated diagonal Fermi contact terms are in good agreement with-experiment, while the calculated off-diagonal Fermi contact terms are in terrible agreement with experiment.