Polymers in flow deform elastically as a result of reduced entropy stored in the distorted chain. Elastic stretching of the chains in flow is assumed; however, measurement of the deformation of individual chains in concentrated solution in flow has largely eluded experiment. Several recent simulations have shown that the chains may compress in flow to elastically deform. Here, we show that polymer chains compress in simple shear flow, using time-resolved fluorescence to measure changes in fluorescence resonance energy transfer of a tagged polymer molecule. Time resolved measurements allow quantitative determination of changes in polymer chain dimensions, and are free from potential artifacts that could affect steady-state fluorescence. Flow-induced chain compression is reconciled with the observed rheological behavior of polymers, namely, shear thinning and elasticity. The ability to understand the flow behavior and model these complex systems will evolve through this important finding. The implications for reptation are profound, as the observed compressive behavior suggests that entanglements are not statistically significant at the concentrations measured.Keywords (keywords): polymer physics; dynamics; elasticity; time-resolved; FRET; Couette flow; shear