A new technique to measure normal stresses in dilute polymer solutions is described. The apparatus developed for this method essentially consists of two closely spaced disks in relative rotation. Fluid is slowly introduced at the center of the disks so that there is a small radial flow superposed on the circumferential motion, and the normal stresses induced in the circumferential direction are detected by measuring the retardation of the radial flow. From such measurements, a fluid relaxation time can be found for each sample and data with dilute Polyox solutions indicate some agreement with predictions from the molecular theory of Rouse.