By combining confocal microscopy and stress assessment from local structural anisotropy, we directly measure stresses in 3D quiescent colloidal liquids. Our noninvasive and nonperturbative method allows us to measure forces 50 fN with a small and tunable probing volume, enabling us to resolve the stress fluctuations arising from particle thermal motions. We use the Green-Kubo relation to relate these measured stress fluctuations to the bulk Brownian viscosity at different volume fractions, comparing against simulations and conventional rheometry measurements. We find that the Green-Kubo analysis gives excellent agreement with these prior results, suggesting that similar methods could be applied to investigations of local flow properties in many poorly understood far-from-equilibrium systems, including suspensions that are glassy, strongly sheared, or highly confined. © 2017 American Physical Society.