Using ideas from statistical nonequilibrium thermodynamics we develop a spatially nonlocal theory of the influence of diffusion on rapid chemical reactions. The new approach generalizes the hydrodynamic (local) theory by including elementary events that influence both diffusion and reaction on molecular length scales and eliminates problems in the local theory that occur at short times. Examples of the nonlocal approach are given for several reaction schemes, including a simple reversible reaction A + B reversible arrow C, and single species reactions of the form A + A --> products. For low densities, the present theory is equivalent to the usual Smoluchowski method. In this regime, an intermediate version of the theory, including only nonlocal effects due to reaction, is compared to the full nonlocal theory and to the earlier hydrodynamic level theory and is shown to produce results for the time dependence of the radial distribution function that are similar at low density to the full theory. The application of the new approach at higher densities and to lower dimensions is described briefly.