  Inelastic x-ray scattering and $ab$-$initio$ calculation are applied to
investigate the lattice dynamics and electron-phonon coupling of the ternary
silicide superconductor CaAlSi ($P/bar{6}m2$). A soft c-axis polarized mode is
clearly observed along the $/Gamma$-$A$-$L$ symmetry directions. The soft mode
is strongly anharmonically broadened at room temperature, but, at 10 K, its
linewidth narrows and becomes in good agreement with calculations of linear
electron-phonon coupling. This establishes a coherent description of the
detailed phonon properties in this system and links them clearly and
consistently with the superconductivity.
