  Chiral higher-spin gravity is a higher-spin extension of both self-dual
Yang-Mills and self-dual gravity and is a unique local higher-spin gravity in
four dimensions. Its existence implies that there are two closed subsectors in
Chern-Simons matter theories. We make first steps in identifying these
(anti-)chiral subsectors directly on the CFT side, which should result in a
holographically dual pair where both sides are nontrivial, complete, yet
exactly soluble. We also discuss closely related theories: self-dual Yang-Mills
(SDYM) and self-dual gravity (SDGR) in the holographic context.
