  In this note we investigate the generalized massive gravity in asymptotically
$AdS_3$ spacetime by combining the two mass terms of topological massive
gravity and new massive gravity theory. We study the linearized excitations
around the $AdS_3$ background and find that at a specific value of a certain
combination of the two mass parameters (chiral line), one of the massive
graviton solutions becomes the left moving massless mode. It is shown that the
theory is chiral at this line under Brown-Henneaux boundary condition. Because
of this degeneration of the gravitons the new log solution which has a
logarithmic asymptotic behavior is also a solution to this gravity theory at
the chiral line. The log boundary condition which was proposed to accommodate
this log solution is proved to be consistent at this chiral line. The resulting
theory is no longer chiral except at a special point on the chiral line, where
another new solution with log-square asymptotic behavior exists. At this
special point, we prove that a new kind of boundary condition called log-square
boundary condition, which accommodates this new solution, can be consistent.
