  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.
