  We analyse the divergences of the three-loop partition function at fixed area
in 2D quantum gravity. Considering the Liouville action in the Kahler
formalism, we extract the coefficient of the leading divergence in $\sim
A\Lambda^2 (\ln A\Lambda^2)^2$. This coefficient is non-vanishing. We discuss
the counterterms one can and must add and compute their precise contribution to
the partition function. This allows us to conclude that every local and
non-local divergence in the partition function can be balanced by local
counterterms, with the only exception of the maximally non-local divergence
$(\ln A\Lambda^2)^3$. Yet, this latter is computed and does cancel between the
different three-loop diagrams. Thus, requiring locality of the counterterms is
enough to renormalize the partition function. Finally, the structure of the new
counterterms strongly suggests that they can be understood as a renormalization
of the measure action.
