The formulation and results of a dynamical quasiclassical calculation of the reactive scattering of K+CH3I to yield KI+CH3 are reported. With a Blais-Bunker interaction potential UB and the approximation that the CH3 group can be treated as a single atom, Hamilton's equations of motion are solved to determine collision trajectories as a function of initial conditions. By appropriate Monte Carlo averaging over certain of the initial variables, the desired attributes of the reactive scattering are evaluated; these include the total reaction cross section S r, the differential reaction cross section σ r(θ), the partitioning of the exothermicity of the reaction among the degrees of freedom of the products, and the distribution of angular momentum between the products molecule (J′) and relative orbital motion (L′). A detailed examination is made of the relation between the results obtained from two-dimensional (2-D) and from three-dimensional (3-D) trajectories. It is found that, although Sr and the energy partitioning are similar in the 2-D and 3-D cases, the form of σr(θ) and the angular momentum distribution are different. Comparison with the crossed molecular-beam data available for this system shows that the 3-D calculation with the potential UB yields a reasonable reaction-energy distribution, but total and differential cross sections in disagreement with the experimental information; i.e., Sr equals 400 Å2 instead of the measured value of 7 Å2, and σr(θ) is independent of angle instead of being strongly peaked in the backward direction. An analysis of the scattering trajectories shows that the erroneous results derive from the neglect in the interaction potential of an attenuation factor that decreases the K, I attraction for an I atom that is part of a CH3I molecule. Introduction of such a three-body term yields cross sections and energy distributions in qualitative agreement with the experimental data. Additional measurements are required to test the theoretical angular momentum distribution.