We report the first direct, quantitative measurements of the shear aligning properties of a main-chain thermotropic liquid crystalline polymer (LCP). We find that a model thermotrope with alternating mesogen and spacer structure is of the shear aligning type throughout its nematic range. The director rotates uniformly in the shear flow toward the Leslie alignment angle as probed by in situ flow conoscopy. The Leslie alignment angle becomes progressively closer to the flow direction as temperature decreases, corresponding to a decrease of the tumbling parameter lambda with increasing order parameter S. Our measurements of lambda (S) enable direct comparison with predictions from molecular models, which predict that shear alignment prevails in the limit of flexible nematic chains. This is in direct contrast to rodlike lyotropic LCPs for which director tumbling is the rule.