A radially sheared azimuthal flow is observed in a cylindrical helicon plasma device. The shear flow is roughly azimuthally symmetric and contains both time-stationary and slowly varying components. The turbulent radial particle flux is found to peak near the density gradient maximum and vanishes at the shear layer location. The shape of the radial plasma potential profile associated with the azimuthal E × B flow is predicted accurately by theory. The existence of the mean shear flow in a plasma with finite flow damping from ion–neutral collisions and no external momentum input implies the existence of radial angular momentum transport from the turbulent Reynolds-stress.