The gas-phase S(N)2 reaction Cl-+CH3Br(v,k)-->ClCH3(v'k')+Br-has been studied using reduced dimensionality time independent quantum scattering theory. The C-Br and C-Cl stretching degrees of freedom (quantum numbers v and v') and the azimuthal angle (rotation of the CH3 group; quantum numbers k and k') are treated explicitly. An infinite order sudden approximation and Radau coordinates for the stretching modes are used. The scattering problem is formulated in hyperspherical coordinates. A potential energy surface of Wang, Zhu, and Hase is used. It is found that this surface can reproduce the experimentally observed independence of the rate constant on the internal temperature of CH3Br only if it is scaled to enable the transition state geometry to agree with high level ab initio data. The reaction cross sections show the propensity rule Delta k=0 for the azimuthal rotation.