We used both conventional rheometry and nuclear magnetic resonance (NMR) velocimetry to study shear banding in a solution of 200 mM cetylpyridinium chloride and 120 mM sodium salicylate in 0.5 M sodium chloride. The solution behaved as a Maxwell fluid up to frequencies of 10 Hz. Theoretical predictions of critical strain rate and shear stress were in good agreement with measurements obtained using controlled strain rate rheometry. Using NMR velocimetry, we observed convincing evidence of shear banding in capillary flow with a band of very high, approximately constant, shear rate next to the wall that grew in thickness with increasing apparent shear rate. We believe that the shear rate in this band ( similar to 600 s(-1)) marks the beginning of the hypothesized high shear rate limb of the flow curve. We also observed shear banding in both the cylindrical Couette and cone-and-plate geometries. Shear banding started at shear rates that were approximately the same as the critical shear rate measured with the mechanical rheometer. With increasing shear rate in the fluid, more than two shear bands were sometimes evident, although they exhibited dynamical instabilities. That is, the highest shear rate band was variable in both magnitude and position.