An effective two-dimensional potential energy surface has been constructed for the S(N)2 reaction Cl-+CH3Br-->ClCH3+Br- from coupled-cluster calculations with a large basis set. In the quantum dynamics calculations Radau coordinates were employed to describe the Cl-C and C-Br stretching modes. Making use of the filter diagonalization method and an optical potential, bound states as well as resonance states up to energies far above the dissociation threshold have been calculated. The resonance widths fluctuate over several orders of magnitude. In addition to a majority of Feshbach-type resonances there are also exceedingly long-lived shape resonances, which can only decay by tunneling. Owing to a smaller width of the potential barrier and a larger density of states, tunneling through the barrier is more important for Cl-+CH3Br than for Cl-+CH3Cl despite the larger total mass of this system. Excitation of the C-Br stretching vibration enhances the tunneling probability of the entrance channel complex.