The orientational response of a liquid crystalline polymer (LCP) solution, specifically poly(benzyl L-glutamate) (PBLG) in deuterated benzyl alcohol, to the application of a sheat field has been determined by in-situ neutron scattering. By analyzing the anisotropic two-dimensional scattering pattern, the orientation of the LCP at different shear rates, gamma, in the now-vorticity plane was determined. It was found that the LCP response has three regimes. At low sheat rates, gamma < gamma(1), the orientation of the LCP molecule increases with gamma, at intermediate flow rates, gamma(1) < gamma < gamma(2), there is not much change in the orientation of the PBLG molecule with gamma, and at high gamma, gamma > gamma(2), there is again an increase in the orientation of the LCP with shear rate. The crossover shear rates, gamma(1), and gamma(2), have been shown to correlate well to the first two relaxation times of a rodlike polymer in concentrated solution. The results are also compared and contrasted to some recent studies of the theology of LCP in solution.