Hydrodynamics and collision-dominated transport are crucial to understand the slow dynamics of many correlated quantum liquids. The ratio eta/s of the shear viscosity eta to the entropy density s is uniquely suited to determine how strongly the excitations in a quantum fluid interact. We determine eta/s in clean undoped graphene using a quantum kinetic theory. As a result of the quantum criticality of this system the ratio is smaller than in many other correlated quantum liquids and, interestingly, comes close to a lower bound conjectured in the context of the quark gluon plasma. We discuss possible consequences of the low viscosity, including preturbulent current flow.