Femtosecond laser pulses and coherent two-phonon Raman scattering were used to excite KFaO(3) into a squeezed state, nearly periodic in time, in which the variance of the atomic displacements dips below the standard quantum limit for half of a cycle. This nonclassical state involves a continuum of transverse acoustic modes that leads to oscillations in the refractive index associated with the frequency of a van Hove singularity in the phonon density of states.