We investigate the effects of spatial heterogeneity on the coexistence of competing species in the case when the heterogeneity is dynamically generated by environmental flows with chaotic mixing properties. We show that one of the effects of chaotic advection on the passively advected species (such as phytoplankton, or self-replicating macromolecules) is the possibility of coexistence of more species than that limited by the number of niches they occupy. We derive a novel set of dynamical equations for competing populations. ; Comment: 14 pages, with 7 embedded figures, submitted for publication