The beaming pattern produced by a relativistically moving blob of isotropic nonthermal electrons that Thomson-scatter photons from an external isotropic radiation field goes as D4+2α. Here D is the Doppler factor, and α is the energy spectral index of the radiation. This differs from the well-known beaming pattern produced by radiation emitted isotropically in the blob frame, which is ∝ D3+α. This result is important for treatments of blazar statistics, beaming constraints, and tests of gamma-ray source models.