We investigate the chirality of phonon modes in twisted bilayer WSe2. We demonstrate distinct chiral behavior of the K/K valley phonon modes for twist angles close to 0 • and close to 60 • . Moreover, we discover two sets of well-separated chiral valley modes in moiré lattices for angles close to 60 • . These emergent moiré chiral valley phonons originate from inversion symmetry breaking at the moiré scale. We also find similar emergent chiral modes in moiré patterns of strain-engineered bilayer WSe2 and MoSe2/WSe2 heterostructure. Furthermore, we observe the flattening of bands near the phononic band-gap edges for a broad range of twist angles in twisted bilayer WSe2. Our findings, which are expected to be generic for moiré systems composed of two-dimensional materials that break inversion symmetry, are relevant for understanding electron-phonon and exciton-phonon scattering, and for designing phononic crystals to mimic behaviors of electrons in moiré materials.