A parallel-competitive reaction system, A + B-1 --> 2P and A + B-2 --> 2W, where A and B-1 are the reactants, B-2 is a reactive impurity, P is the desired product, and W is a byproduct, is simulated in a chaotic flow by solving the differential convection-diffusion-reaction equations. Three different flow conditions are investigated: a predominantly regular system, a globally chaotic flow, and an intermediate case that displays predominantly chaotic behavior but which has four small islands of regular flow. The time evolution and spatial distribution of species concentration depend strongly both on the nature of the flow and on the relative rates of the two reactions. Even in the globally chaotic flow, significant spatial heterogeneity exists throughout the duration of the reactive mixing simulation. Product and waste accumulate in different spatial regions, depending on the relative characteristic times of the two reactions. When the primary reaction is the faster one, waste tends to accumulate in local A-rich regions and the selectivity of product to waste is strongly affected by the degree of chaos in the system. On the other hand, when the side reaction is faster, waste accumulates in segregated regions which have local excesses of B-2, but mixing has minimal effect on the quantity of waste produced.