We present a quantum dynamics study of the Cl+CH(4)reversible arrow HCl+CH3 reaction using a four-dimensional rotating bond umbrella (RBU) model. A semiempirical potential energy surface is employed, where the zero point energy of the modes not explicitly treated in the RBU calculations is approximately included. The potential gives a vibrationally adiabatic ground state barrier height of 3.48 kcal/mol. The calculations have been performed in hypercylindrical coordinates using a log-derivative method. A single sector hyperspherical projection method has been developed for applying boundary conditions. A guided spectral transform (GST) Krylov subspace method has been constructed to find the eigenstates of the coupling matrix appearing in the coupled channel equations. The results show that the product methyl is rotationally cold for the forward reaction. A pronounced tunneling effect on the rate constants was obtained. The calculated thermal rate constants are 12%-45% smaller than the experimental results over the temperature range 200-800 K for the Cl+CH(4)reversible arrow HCl+CH3 reaction. State-to-state differential cross sections have been studied at a kinetic energy of 0.159 eV. A detailed comparison with experimental measurements is made.