Many energy, environmental, industrial, and microfluidic processes rely on the viscous flow of polymer solutions through confined and tortuous spaces. These fluids are typically shear-thinning; however, unexpectedly, these solutions can flow thicken—that is, the macroscopic flow resistance abruptly increases above a threshold flow rate—but only in a confined, tortuous space, not in bulk solution. The reason why has been a puzzle for over half a century. In this talk, I will describe how by directly visualizing the flow in a transparent 3D porous medium, we have shown that this anomalous flow thickening reflects the onset of an elastic instability in which the fluid exhibits chaotic spatiotemporal velocity fluctuations reminiscent of inertial turbulence, despite the vanishingly small Reynolds number. Our measurements help characterize the onset and characteristics of this fascinating flow state, helping to deepen understanding of complex fluid flows in confinement and providing guidelines for predicting and controlling these flows in applications.