The Einstein-aether theory provides a simple, dynamical mechanism for breaking Lorentz invariance. It does so within a generally covariant context and may emerge from quantum effects in more fundamental theories. The theory leads to a preferred frame and can have distinct experimental signatures. In this Letter, we perform a comprehensive study of the cosmological effects of the Einstein-aether theory and use observational data to constrain it. Allied to previously determined consistency and experimental constraints, we find that an Einstein-aether universe can fit experimental data over a wide range of its parameter space, but requires a specific rescaling of the other cosmological densities.