Valley degrees of freedom in transition-metal dichalcogenides influence thoroughly electron-phonon coupling and its nonequilibrium dynamics. We conducted a first-principles study of the quantum kinetics of chiral phonons following valley-selective carrier excitation with circularly-polarized light. Our numerical investigations treat the ultrafast dynamics of electrons and phonons on equal footing within a parameter-free ab-initio framework. We report the emergence of valley-polarized phonon populations in monolayer MoS$_2$ that can be selectively excited at either the K or K' valleys depending on the light helicity. The resulting vibrational state is characterized by a distinctive chirality, which lifts time-reversal symmetry of the lattice on transient timescales. We show that chiral valley phonons can further lead to fingerprints of vibrational dichroism detectable by ultrafast diffuse scattering and persisting beyond 10 ps. The valley polarization of nonequilibrium phonon populations could be exploited as information carrier, thereby extending the paradigm of valleytronics to the domain of vibrational excitations.
