  We report high-resolution inelastic x-ray measurements of the soft phonon
mode in the charge-density-wave compound TiSe$_2$. We observe a complete
softening of a transverse optic phonon at the L point, i.e. q = (0.5, 0, 0.5),
at T ~ T_{CDW}. Renormalized phonon energies are observed over a large
wavevector range $(0.3, 0, 0.5) \le \mathbf{q} \le (0.5, 0, 0.5)$. Detailed
ab-initio calculations for the electronic and lattice dynamical properties of
TiSe2 are in quantitative agreement with experimental frequencies for the
phonon branch involving the soft mode. The observed broad range of renormalized
phonon frequencies is directly related to a broad peak in the electronic
susceptibility stabilizing the charge-density-wave ordered state. Our analysis
demonstrates that a conventional electron-phonon coupling mechanism can explain
a structural instability and the charge-density-wave order in TiSe_2 although
other mechanisms might further boost the transition temperature.
