We study the effect of a linear shear flow on a collection of interacting active, self-propelled particles modeled via the Vicsek model. The imposed flow has a dramatic effect on the behavior of the model. We find that in the presence of shear there is no order-disorder transition, and that coarsening of the domains is arrested. Shear also suppresses the so-called giant density fluctuations that are observed in the quiescent limit.