We image the flow of a nearly random close packed, hard- sphere colloidal suspension (a "paste") in a square capillary using confocal microscopy. The flow consists of a "plug" in the center while shear occurs localized adjacent to the channel walls, reminiscent of yield-stress fluid behavior. However, the observed scaling of the velocity profiles with the flow rate strongly contrasts yield-stress fluid predictions. Instead, the velocity profiles can be captured by a theory of stress fluctuations originally developed for chute flow of dry granular media. We verified this both for smooth and rough walls.