Optical selection rules in monolayers of transition metal dichalcogenides and of their heterostructures are determined by the conservation of the z-component of the total angular momentum—J Z = L Z +S Z – associated with the C3 rotational lattice symmetry which assumes half integer values corresponding, modulo 3, to distinct states. Here we show, based on polarization resolved and low temperature magneto-optical spectroscopy experiments, that the conservation of the total angular momentum in these systems leads to a very efficient exciton-phonon interaction when the coupling is mediated through chiral phonons. We identify these phonons as the Γ point E" modes which despite carrying angular momentum ± 1 are able to induce an excitonic spin-flip of $mp2$ thanks to the C3 symmetry. These experiments reveal the crucial role of electron-phonon interaction in the carrier dynamics of group 6 transition metal dichalcogenides.