  Higher Spin Gravities are scarce, but covariant actions for them are even
scarcer. We construct covariant actions for contractions of Chiral Higher Spin
Gravity that represent higher spin extensions of self-dual Yang-Mills and
self-dual Gravity theories. The actions give examples of complete higher spin
theories both in flat and (anti)-de Sitter spaces that feature gauge and
gravitational interactions. The actions are based on a new description of
higher spin fields, whose origin can be traced to early works on twistor
theory. The new description simplifies the structure of interactions. In
particular, we find a covariant form of the minimal gravitational interaction
for higher spin fields both in flat and anti-de Sitter space, which resolves
some of the puzzles in the literature.
