Materials subjected to a magnetic field exhibit the Hall effect, a phenomenon studied and understood in fine detail. Here we report a qualitative breach of this classical behavior in electron systems with high viscosity. The viscous fluid in graphene is found to respond to non-quantizing magnetic fields by producing an electric field opposite to that generated by the classical Hall effect. The viscous contribution is large and identified by studying local voltages that arise in the vicinity of current-injecting contacts. We analyze the anomaly over a wide range of temperatures and carrier densities and extract the Hall viscosity, a dissipationless transport coefficient that was long identified theoretically but remained elusive in experiment. Good agreement with theory suggests further opportunities for studying electron magnetohydrodynamics.
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