The effects of diffusion and convection on the evolution of reactions in chaotic flows are examined. Direct numerical simulations are applied to compute the evolution of the mixing structure, describe the stretching field, and solve the convection-reaction-diffusion material balance in a periodic, 2-D chaotic flow with an instantaneous, bimolecular reaction: A + B --> 2P. These computations demonstrate that the location of the reactive zones in the flow can be predicted from the stretching field. The time-evolution of the concentration profiles approaches an invariant shape when the time scale of the convective and diffusive mixing processes are comparable. Under such conditions, exponential stretching and its consequence, asymptotic directionality, are the mechanisms controlling the evolution of chaotic reactive systems.