Fully atomistic molecular dynamics computer simulations of cis-polyisoprene melts have been performed. Two different methods were used to generate four initial configurations. The local polymer dynamics were substantially independent of initial chain configuration. The ratios of correlation times for different C-H vectors in the chain backbone match experiment very well. Absolute correlation times from the simulation are about 2.5 times slower than experimental values. The correlation functions obtained from the simulations are strongly non-exponential, in general agreement with experiment. The local dynamics in these simulations are fairly isotropic, in marked contrast to results reported from simulations of polyethylene melts by Takeuchi and Roe. Several analysis techniques indicate that the spatial extent of the cooperative motion that accompanies conformational transitions in polyisoprene melts is about 1-2 repeat units. A similar length scale was found recently in simulations of polyisoprene in a dilute solution.