  We present a detailed study of the electric dipole moment of the neutron
induced by a vacuum theta angle within the framework of QCD sum rules. At
next-to-next-to leading order in the operator product expansion, we find the
result d_n(\theta) = 2.4 x 10^{-16} \theta e cm, to approximately 40%
precision. With the current experimental bound this translates into a limit on
the theta parameter of |\theta| < 3 x 10^{-10}. We compare this result with the
long-standing estimates obtained within chiral perturbation theory, and observe
a numerical similarity, but also significant differences in the source of the
dominant contribution.
