  We study the topologically massive gravity at the chiral point (chiral
gravity) by using the logarithmic conformal field theory. Two new tensor fields
of $\psi^{new}$ and $X$ are introduced for a candidate of propagating physical
field at the chiral point. However, we show that ($\psi^{new},\psi^L$) form a
dipole ghost pair of unphysical fields and $X$ is not a primary. This implies
that there is no physically propagating degrees of freedom at the chiral point.
