  Manipulating materials properties far from equilibrium recently garnered
significant attention, with experimental emphasis on transient melting,
enhancement, or induction of electronic order. A more tantalizing aspect of the
matter-light interaction regards the possibility to access dynamical steady
states with distinct non-equilibrium phase transitions to affect electronic
transport. Here, we show that the interplay of crystal symmetry and optical
pumping of monolayer transition-metal dichalcogenides (TMDCs) provides a novel
avenue to engineer topologically-protected chiral edge modes. In stark contrast
to graphene and previously-discussed toy models, the underlying generic
mechanism relies on the intrinsic three-band nature of TMDCs near the band
edges. Photo-induced band inversions scale linearly in applied pump field and
exhibit a transition from one to two chiral edge modes upon sweeping from red
to blue detuning. We develop a strategy to understand non-equilibrium
Floquet-Bloch bands and topological transitions directly from ab initio
calculations, and illustrate for the example of WS$_2$ that control of chiral
edge modes can be dictated solely from symmetry principles and is not
qualitatively sensitive to microscopic materials details.
