  In this paper, we study the spin-3 topological massive gravity(TMG), paying
special attention to its properties at the chiral point. We propose an action
describing the high spin fields coupled to TMG. We discuss the spin-3
fluctuations around the AdS$_3$ vacuum and find that there is an extra local
massive mode, besides the left-moving and right-moving boundary massless modes.
At the chiral point, such extra mode becomes massless and degenerates with the
left-moving mode. We show that at the chiral point the only degrees of freedom
in the theory are the boundary right-moving graviton and spin-3 field. We
conjecture that spin-3 chiral gravity with Brown-Henneaux boundary condition is
holographically dual to 2D chiral CFT with classical $W_3$ algebra and central
charge $c_R=3l/G$.
