The equation-of-motion coupled cluster method (EOMIP) using a reference Slater determinant based on the CH3S--anion ground state with basis sets of triple- and quadruple-zeta quality was applied for numerical optimizations of geometries of stationary points on adiabatic Jahn-Teller surfaces of the (XE)-E-2 ground state of CH3S crossing at the C-3v symmetry nuclear configuration. Calculations by the multireference configuration interaction method and multiconfiguration quasi-degenerate second-order perturbation (PT2) theory were also performed with use of a complete active space CASSCF reference wave function. The linear and quadratic Jahn-Teller constants were computed for each of three Jahn-Teller active modes. The potential surfaces corresponding to spin-orbit state E-2(3/2) and E-2(1/2) were obtained with eigenenergies of the full Breit-Pauli spin-orbit operator with a PT2-CASSCF reference wave function. The one- and two-electron scalar relativistic effects were included in CASSCF and spin-orbit calculations. The calculated Jahn-Teller stabilization energy, the barrier to pseudorotation, and the spin-orbit splitting are 93, 15, and 358 cm(-1), respectively. The Jahn-Teller distortions are totally quenched by the strong spin-orbit coupling. The recommended values of the geometry parameters of CH3S are R-e(CS) = 1.794 Angstrom, R-e(CH) = 1.087 Angstrom, and alpha(e)(HCS) = 109.8degrees.