Toward a twistor action for chiral higher-spin gravity

A covariant twistor action for chiral higher-spin theory in (A)dS and flat space is constructed in terms of a holomorphic Chern-Simons theory on twistor space. The action reproduces all known cubic vertices of chiral higher-spin theory in flat space. The spacetime action of the holomorphic Chern-Simons theory in flat space is also obtained.