  We propose a mechanism for light-induced unconventional superconductivity in
a two-valley semiconductor with a massive Dirac type band structure. The
superconducting phase results from the out-of-equilibrium excitation of
carriers in the presence of Coulomb repulsion and is stabilized by coupling the
driven semiconductor to a bosonic or fermionic thermal bath. We consider a
circularly-polarized light pump and show that by controlling the detuning of
the pump frequency relative to the band gap, different types of chiral
superconductivity would be induced. The emergence of novel superconducting
states, such as the chiral $p$-wave pairing, results from the Floquet
engineering of the interaction. This is realized by modifying the form of the
Coulomb interaction by projecting it into the states that are resonant with the
pump frequency. We show that the resulting unconventional pairing in our system
can host topologically protected chiral bound states. We discuss a promising
experimental platform to realize our proposal and detect the signatures of the
emergent superconducting state.
