Rheological measurements are reported for a fully nematic thermotropic liquid crystalline copolyester composed of 80%p‐hydroxybenzoic acid/20% poly(ethylene terephthalate). The polymer displays shear thinning behavior with a constant power‐law index over eight decades of shear rate; no shear‐independent plateau (region II) is observed. Dynamic time sweeps indicate a high sensitivity of the rheological parameters to thermal history, apparently resulting from crystalline annealing. These annealing effects could be erased by appropriate thermal cycling. Torsional measurements (cone‐and‐plate) were limited at high shear rates by the occurrence of edge fracture. This instability was typically accompanied by an unusual sample texture composed of concentric rings, which was particularly distinct when offgassing had occurred in the polymer melt.