We present experimental and theoretical results on the shear thinning of electrorheological fluids. Rheological measurements on a model fluid consisting of monodisperse silica spheres immersed in a dielectric liquid show a power-law dependence-mu is-proportional-to gamma(-DELTA) of the apparent viscosity-mu on the strain rate-gamma, with DELTA in the range DELTA = 0.68-0.93. We present a theoretical treatment of steady-state cluster formation in applied electric and shear fields, which correctly predicts the observed power-law shear thinning, albeit with an exponent DELTA = 2/3 . We observe no true yield stress in this material.