Cu2ZnSnS4 (CZTS) is a promising material for photovoltaic and thermoelectric applications. Issues with quaternary semiconductors include chemical disorder (e.g., Cu–Zn antisites) and disproportionation into secondary phases (e.g., ZnS and Cu2SnS3). To provide a reference for the pure kesterite structure, we report the vibrational spectra—including both infra-red and Raman intensities—from lattice-dynamics calculations using first-principles force constants. Three-phonon interactions are used to estimate phonon lifetimes (spectral linewidths) and thermal conductivity. CZTS exhibits a remarkably low lattice thermal conductivity, competitive with high-performance thermoelectric materials. Transition from the sulfide to selenide (Cu2ZnSnSe4) results in softening of the phonon modes and an increase in phonon lifetimes.