Pressure-driven flows of high molecular weight polyacrylamide solutions are examined in nanoslits using fluorescence photobleaching. The effective viscosity of polymer solutions decreases when the channel height decreases below the micron scale. In addition, the apparent slippage of the solutions is characterized macroscopically on similar surfaces. Though slippage can explain qualitatively the effective viscosity reduction, a quantitative comparison shows that the slip length is greatly reduced below the micron scale. This result indicates that chain migration is suppressed in confined geometries.