  A hard three-loop correction to parapositronium energy levels of order
$m\alpha^7$ is calculated. This nonlogarithmic contribution is due to the
insertions of one-loop photon propagator in the fermion lines in the diagrams
with virtual two-photon annihilation. We obtained $\Delta
E=0.03297(2)(m\alpha^7/\pi^3)$ for this energy shift.
