Quantum scattering calculations on the S(N)2 reaction Cl- + CH3Cl-->ClCH3+Cl- are reported. The rotating bond approximation (RBA) has been adapted so that three degrees of freedom including the C-Cl stretching vibration and the CH3 umbrella mode are treated explicitly. The calculations have been done with minor modifications of a potential due to Vande Linde and Hase. It is found that initial excitation of the C-Cl vibration has a large effect on the reaction probabilities, while excitation of the CH3 umbrella vibration is less significant. The reaction is dominated by scattering resonances with lifetimes ranging from 0.1 to 10 ps. It is found that the length of the C-Cl bond at the transition state of the reaction has a particularly pronounced effect on the reaction probabilities. The magnitude of the quantum reaction probabilities compares quite well with those calculated using the quasiclassical trajectory method.