While director tumbling is responsible for much of the unique rheological behavior of lyotropic liquid-crystalline polymers (LCPs), it is not clear whether tumbling routinely occurs in main-chain thermotropes. We present experiments on a model thermotropic LCP under shear, using in-situ X-ray scattering as a probe of molecular orientation. This model LCP, PSHQ6-12, was synthesized by Chang and Han [Macromolecules 1996, 29, 2383] and consists of rigid mesogens randomly copolymerized with flexible spacer chains of two different lengths. This architecture suppresses crystallization and lowers the nematic-isotropic transition temperature to an accessible level, allowing a well-defined thermal history to be established prior to now. We present measurements of molecular orientation in steady shear flow, during relaxation, and during shear flow start-up. The evolution of molecular orientation observed during now inception and the observation of shear-induced transparency in the material lead to the hypothesis that PSHQ6-12 is shear aligning rather than tumbling. Consequences of this hypothesis are explored by polydomain simulations based on Ericksen＇s transversely isotropic fluid model, which are capable of capturing many aspects of the experimentally observed rheology and shear-induced structure.