Chirality characterizes an object that is not identical to its mirror image. In condensed matter physics, Fermions have been demonstrated to obtain chirality through structural and time-reversal symmetry breaking. These systems display unconventional electronic transport phenomena such as the quantum Hall effect and Weyl semimetals. However, for bosonic collective excitations in atomic lattices, chirality was only theoretically predicted and has never been observed. We experimentally show that phonons can exhibit intrinsic chirality in monolayer tungsten diselenide, whose lattice breaks the inversion symmetry and enables inequivalent electronic K and -K valley states. The time-reversal symmetry is also broken when we selectively excite the valley polarized holes by circularly polarized light. Brillouin-zone-boundary phonons are then optically created by the indirect infrared absorption through the hole-phonon interactions. The unidirectional intervalley transfer of holes ensures that only the phonon modes in one valley are excited. We found that such photons are chiral through the transient infrared circular dichroism, which proves the valley phonons responsible to the indirect absorption has non-zero pseudo-angular momentum. From the spectrum we further deduce the energy transferred to the phonons that agrees with both the first principle calculation and the double-resonance Raman spectroscopy. The chiral phonons have significant implications for electron-phonon coupling in solids, lattice-driven topological states, and energy efficient information processing.