How anisotropic is our Universe?

Large-scale cosmic microwave background anisotropies in homogeneous, globally anisotropic cosmologies are investigated. We perform a statistical analysis in which the 4-yr data from the Cosmic Background Explorer satellite is searched for the specific anisotropy patterns predicted by these models and thereby set definitive upper limits on the amount of shear, (sigma/H)(0), and vorticity, (omega/H)(0), which are orders of magnitude stronger than previous constraints. We find that primordial anisotropy should have been fine tuned to be less than 10(-3) of its natural value in the Planck era.