  We consider the holographic renormalization group (RG) flow in three
dimensional gravity with the gravitational Chern-Simons term coupled to some
scalar fields. We apply the canonical approach to this higher derivative case
and employ the Hamilton-Jacobi formalism to analyze the flow equations of two
dimensional field theory. Especially we obtain flow equations of Weyl and
gravitational anomalies, and derive $c$-functions for left and right moving
modes. Both of them are monotonically non-increasing along the flow, and the
difference between them is determined by the coefficient of the gravitational
Chern-Simons term. This is completely consistent with the Zamolodchikov's
$c$-theorem for parity-violating two-dimensional quantum field theories.
