Solute mixing in fluids is enhanced significantly by chaotic advection, the phenomenon in which fluid pathlines completely fill the spatial domain explored by a laminar flow. Steady groundwater flows are, in general, not well conditioned for this phenomenon because Darcy's law confines them spatially to nonintersecting stream surfaces. Unsteady groundwater flows, however, may, in principle, induce chaotic solute advection if their time dependence is periodic and produces frequent reorientation of pathlines, an effect connected closely to the development of high solute mixing efficiencies. In this paper, a simple, two-dimensional model groundwater system is studied theoretically to evaluate the possibility of inducing chaotic solute advection in the flow field near a recirculation well whose pumping behavior is time periodic. In the vernacular of dynamical systems theory the model studied is an example of a Hamiltonian system, thus allowing a mathematical formulation that facilitates consideration of whether chaotic advection can occur. When the model system is driven time periodically by alternate operation of the production and injection components of the recirculation well, numerical simulations of the fluid pathlines indicate that regions of chaotic solute advection will, indeed, develop in the flow field near the well, with expected major improvement in plume spreading.