Using deuterium NMR spectroscopy in a Couette cell, we observe shear-induced nematic ordering in the concentrated wormlike-micelle system CTAB/D(2)O, and our results are qualitatively consistent with birefringence studies, and in exact quantitative agreement with the degree of order measured in neutron-diffraction measurements. The width of the nematic region depends on shear rate, as well as on the temperature proximity to the equilibrium isotropic-nematic transition. Comparison of the nematic order profiles with velocity profiles obtained under identical conditions shows quite clearly that the nematic state is not identifiable with a highly sheared, low viscosity layer, and we conclude that the process of shearing induces a nematic state of high viscosity, possibly associated with mesoscale ordering. We present a simple model in which transition from the high shear branch to the viscous nematic branch is counterbalanced by subsequent relaxation of nematic order.