The interplay between lattice and electron degrees of freedom gives rise to complex ordered states in quantum materials. Here, we use high-resolution optical spectroscopy to probe the symmetry of the charge density wave state of 1T-TiSe₂, which is hotly debated. We uncover a previously unobserved, but clear splitting of a doubly degenerate Eu optical phonon, which occurs at the charge-density-wave transition and constitutes direct evidence for the breaking of three-fold rotational symmetry. This rules out the previously proposed P-3c1 structure and is consistent with a low-temperature chiral charge-ordered state as well as a nematic triple-Q state. We highlight the use of high temperature resolution in tracking the evolution of optical phonons, combined with group theoretical analysis, to act as a sensitive bulk probe of subtle symmetry breaking.