The transient extensional viscosity of the nematic melt of thermotropic liquid crystalline (LCP) copolyester Vectra A950 was measured in uniaxial extensional flow in a commercial constant strain rate rheometer. For extension rates between 0.005 and 1 s(-1) the extensional viscosity of Vectra A950 does not reach steady state for Hencky strains up to three to four units, where most samples break. If the viscosity at a certain value of strain is plotted versus the strain rate, a rate-thinning curve is obtained. The extensional viscosity is much higher than three times the sheer viscosity over a broad range of accumulated strain, while injection molded samples always show higher viscosity than compressed samples. The theory developed by Larson and Doi [Larson, R. L. and M. Doi, J. Rheol. 35, 539-563 (1991)] to describe the flow of polydomain LCPs has been adapted for use in elongational flow. The trends of the predictions agree with the measured stress growth curves. The how seems to be dominated by the effect of the texture. The variation in the viscosity measured in samples prepared by different methods is attributed to the variation in the liquid crystalline structure present in the samples and in particular to the initial domain size.