  We theoretically study laser driven nonequilibrium states in the Kitaev
honeycomb model with a magnetoelectric cross coupling. We show that a
topological spin liquid with a gapless chiral edge mode emerges when we apply
an elliptically or circularly polarized laser. This is a strongly correlated
quantum spin version of the Floquet topological insulator. In the topological
phase, the edge mode is made from Majorana fermions and the bulk has gapped
non-Abelian anyon excitations.
