  We construct a two-dimensional action principle invariant under a spin-three
extension of BMS$_3$ group. Such a theory is obtained through a reduction of
Chern-Simons action with a boundary. This procedure is carried out by imposing
a set of boundary conditions obtained from asymptotically flat spacetimes in
three dimensions. When implementing part of this set, we obtain an analog of
chiral WZW model based on a contraction of $sl(3,\mathbb{R}) \times
sl(3,\mathbb{R})$. The remaining part of the boundary conditions imposes
constraints on the conserved currents of the model, which allows to further
reduce the action principle. It is shown that a sector of this latter theory is
related to a flat limit of Toda theory.
