We use a recently proposed covariant procedure to reduce the Chern-Simons action of three-dimensional higher-spin gravity to the boundary, resulting in a Lorentz covariant action for higher-order chiral scalars. After gauge-fixing, we obtain a higher-derivative action generalizing the $\textit{s}$ = 1 Floreanini-Jackiw and $\textit{s}$ = 2 Alekseev-Shatashvili actions to arbitrary spin s. For simplicity, we treat the case of general spin at the linearized level, while the full non-linear asymptotic boundary conditions are presented in component form for the SL(3, ℝ) case. Finally, we extend the spin-3 linearized analysis to a background with non-trivial higher-spin charge and show that it has a richer structure of zero modes.