The dynamic structure factor of molten CsCl has been measured at low momentum transfer, 1.4 nm(-1) <= Q < 33 nm(-1), using high-resolution inelastic x-ray scattering. The longitudinal acoustic mode disperses 1.7 times faster than the adiabatic sound velocity and its linewidth increases following the Q(2) law as predicted by the hydrodynamics. However, the linewidth is a factor of seven smaller than the estimation using the linewidths obtained from Brillouin light scattering. The large speed-up and the significant narrowing of the collective mode, which can be related to each other by a recently presented viscoelastic theory, must arise from the intrinsic nature of molten alkali chlorides. Furthermore in comparison with the previous results for molten NaCl and KCl, the apparent sound velocity is found to be approximately scaled by the inverse of the square-root of the effective mass among these molten salts.