  We report on the effect of laser illumination with circularly polarized light
on the electronic structure of AB-stacked graphite samples. By using Floquet
theory in combination with Green's function techniques, we find that the
polarized light induces band-gap openings at the Floquet zone edge
$\hbar\Omega/2$, bridged by chiral boundary states. These states propagate
mainly along the borders of the constituting layers as evidenced by the
time-averaged local density of states and the probability current density in
several geometries. Semianalytic calculations of the Chern number suggest that
these states are of topological nature, similar to those found in illuminated
2D samples like monolayer and bilayer graphene. These states are promising
candidates for the realization of a three-dimensional version of the quantum
Hall effect for Floquet systems.
