  Let $G$ be the group of orientation-preserving isometries of a rank-one
symmetric space $X$ of non-compact type. We study local rigidity of certain
actions of a solvable subgroup $\Gamma \subset G$ on the boundary of $X$, which
is diffeomorphic to a sphere. When $X$ is a quaternionic hyperbolic space or
the Cayley hyperplane, the action we constructed is locally rigid.
