Using a recent generalization of fluctuation theory that includes spatially nonlocal effects, we examine the influence of nonlocal chemical reactivities on rapid chemical reactions in two dimensions. We focus attention of the irreversible reaction A + A --> products at low density, exploring the time dependence of the radial distribution of pairs of reactants, its asymptotic time dependence, and steady states in the presence of inputs. As in the case of three dimensions, we find that the nonlocal theory removes inherent problems with the local theory that occur at short times, gives the expected logarithmic divergence in the absence of inputs, but has well-behaved steady state properties in the presence of inputs. Thus, the nonlocal theory appears to provide a systematic method for treating rapid reactions in membranes and on surfaces at higher densities.