This paper proposes a new approach to the hydraulics of in situ groundwater remediation. In situ remediation promotes reactions between an injected treatment solution and the contaminated groundwater, but without a hydraulic mechanism to promote spreading, the laminar flows characteristic of porous media will keep the two fluids in approximately the same relative configuration as they travel through the aquifer, limiting the opportunity for reactions to occur. To address this fundamental limitation, this paper borrows a key result from the fluid mechanics literature: Spreading in laminar flows is optimized by chaotic advection. Previous studies have applied this result to groundwater remediation using the pulsed dipole model, but that model depends on reinjection of fluid, which presents a number of theoretical and practical limitations. Accordingly, this paper proposes a new conceptual model for plume spreading by chaotic advection, using an engineered sequence of extractions and injections of clean water at an array of wells, which generates plume spreading by stretching and folding the fluid interface between the injected treatment solution and the contaminated groundwater but does not require reinjection. The paper includes an overview of the analytical techniques—Poincaré sections, periodic points, stable and unstable manifolds, heteroclinic points, and Lyapunov exponents—used to demonstrate chaotic advection in the limiting case in which diffusion is negligible. Numerical simulations show that spreading by stretching and folding is complimentary to spreading resulting from aquifer heterogeneity.