  A previously proposed all-loop-orders relation between the Regge limits of
four-point amplitudes of N=4 supersymmetric Yang-Mills theory and N=8
supergravity is established at the three-loop level. We show that the Regge
limit of known expressions for the amplitudes obtained using generalized
unitarity simplifies in both cases to a (modified) sum over three-loop ladder
and crossed-ladder scalar diagrams. This in turn is consistent with the result
obtained using the eikonal representation of the four-point gravity amplitude.
A possible exact three-loop relation between four-point amplitudes is also
considered.
