The improvement of continuously variable transmissions (CVTs) is a challenging task. Detailed dynamic models of the system are needed for the optimization process. This paper introduces a new model of a rocker-pin chain, which is the central part of a chain CVT. During the derivation of the equations of motion, special attention is turned on the exact description of the joint kinematics. An interesting method to speed up the numerical simulation of the chain drive is introduced, which takes into account the special structure of the mass matrix. Simulation results show the strong influence of the geometry of the rocker-pin joints on the dynamics of the whole gear. Further reasonable gear efficiencies can be estimated for arbitrary joint geometries. This model is an excellent basis for further work on optimization of the CVT chain.