We have developed a small concentric cylinder Couette cell which fits into the 10 mm sample space of a NMR electromagnet. The 2 mm fluid gap provides sufficiently high shear rates to result in shear‐thinning behavior in polymer solutions, and the limited sample volume makes possible the study of gram quantities of material. By using Fourier encoding for velocity combined with microimaging to 50 μm resolution, we are able to provide precise and accurate maps of velocity across the cell. Profiles obtained from these maps are fitted using a power‐law fluid model to yield the exponentn. For water we obtain 1.0, as expected, while for the polymer solution the effective exponent decreases to around 0.4 as the rotation speed and hence the shear rate, is increased. These data are compared, and found to be consistent with, the results of conventional viscometry using a cone‐and‐plate geometry.