We have measured the shear and complex viscosities of a thermotropic liquid crystalline copolymer ofp‐hydroxybenzoic acid and 2,6‐hydroxynaphthoic acid as a function of capillary diameter and parallel‐plate gap spacing. In constrast to a study by Wissbrun, Kiss, and Cogswell, who reported that the viscosity increases significantly at small gaps, we find no dependence on the capillary diameter and a smalldecreasein complex viscosity with parallel‐plate spacing. In an appendix we address an experimental artifact that can lead to an apparent decrease of the viscosity with gap spacing even for flexible polymers.