  We analyze the symmetry realized asymptotically on the two dimensional
boundary of AdS_3 geometry in topologically massive gravity, which consists of
the gravitational Chern-Simons term as well as the usual Einstein-Hilbert and
negative cosmological constant terms. Our analysis is based on the conventional
canonical method and proceeds along the line completely parallel to the
original Brown and Henneaux's. In spite of the presence of the gravitational
Chern-Simons term, it is confirmed by the canonical method that the boundary
theory actually has the conformal symmetry satisfying the left and right moving
Virasoro algebras. The central charges of the Virasoro algebras are computed
explicitly and are shown to be left-right asymmetric due to the gravitational
Chern-Simons term. It is also argued that the Cardy's formula for the BTZ black
hole entropy capturing all higher derivative corrections agrees with the
extended version of the Wald's entropy formula. The M5-brane system is
illustrated as an application of the present calculation.
