We apply passive probes to protein solutions and evaluate the viscous response to folding and unfolding, allowing us to accurately quantify both the thermodynamics of protein folding and the structural dimensions of the protein molecules with subnanometer resolution. Hard-sphere approximations predict a measurable change in relative viscosity as the hydrodynamic volume fraction of protein molecules increases during unfolding. Microrheology measures these changes to unambiguously evaluate the ensemble average characteristics of the unfolded state in a denaturant, urea, while minimizing the shear-induced unfolding and alignment associated with conventional rheometry.