  We formulate four dimensional higher spin gauge theories in spacetimes with
signature (4-p,p) and nonvanishing cosmological constant. Among them are chiral
models in Euclidean (4,0) and Kleinian (2,2) signature involving half-flat
gauge fields. Apart from the maximally symmetric solutions, including de Sitter
spacetime, we find: (a) SO(4-p,p) invariant deformations, depending on a
continuous and infinitely many discrete parameters, including a degenerate
metric of rank one; (b) non-maximally symmetric solutions with vanishing Weyl
tensors and higher spin gauge fields, that differ from the maximally symmetric
solutions in the auxiliary field sector; and (c) solutions of the chiral models
furnishing higher spin generalizations of Type D gravitational instantons, with
an infinite tower of Weyl tensors proportional to totally symmetric products of
two principal spinors. These are apparently the first exact 4D solutions with
non-vanishing massless higher spin fields.
