For millennia, industrial reactions have relied on the efficient mixing of reagents by using turbulence: a flow phenomenon that provides dynamic chaotic mixing. However, a range of environmental, industrial, and energy processes occur under geometric confinement, where these turbulent mixing enhancements are inaccessible—providing fundamental limits to reaction rates that have persisted for centuries. In this work, we demonstrate how addition of dilute polymers can induce a purely elastic flow instability that produces dynamic chaotic flow fluctuations, even under strong geometric confinement. We show how this elastic instability can mimic the mixing enhancements of turbulence and accelerate a model chemical reaction by 4x while simultaneously increasing reaction throughput by 20x, circumventing traditional tradeoffs. To our knowledge, this is the first demonstration of elastic instabilities providing turbulent-like enhancements to reactive mixing. We thus anticipate this technique to be useful in a broad range of industrial processes: for example, in the production of biopharmaceuticals, or the synthesis or recycling of polymers, which are occur within the confinement of catalytic packed beds or heat exchange reactors. We also anticipate these results to be useful for environmental processes, such as groundwater remediation, where poor dispersive mixing of reactive oxidants limits the degradation of trapped contaminants.