The interfacial shear stress that occurs when a network of a polymer that is highly mobile at the segment level (an elastomer) is slid over a smooth surface of an immobile (glassy) polymer has been measured. The glassy material is covered by a thin layer of end-attached chains of the mobile material. The experiment was designed so that there were no free chains at the interface; the slip occurred between network chains on the one side and rigid material plus end-attached mobile chains on the other side. Two main results were obtained. (i) The interfacial shear stress is strongly affected by the segment mobility of the materials on both sides of the slip plane, and considerably lower stress is observed when the materials on both sides of the interface are highly mobile. (ii) Very thin layers of tethered chains can increase the interfacial friction. Both results are relevant to the understanding of a number of practical situations that range from the operation of thin layers of lubricants, such as those found in magnetic storage devices, to the problem of wall slip and melt fracture in polymer processing.