  We present an effective field theory for the crystalline color
superconductivity phase of QCD. It is kown that at high density and at low
temperature QCD exhibits a transition to a color superconducting phase
characterized by energy gaps in the fermion spectra. Under specific
circumstances the gap parameter has a crystalline pattern, breaking
translational and rotational invariance. The corresponding phase is the
crystalline color superconductive phase (or {\it LOFF} phase). We compute the
parameters of the low energy effective lagrangian describing the motion of the
free phonon in the high density medium and derive the phonon dispersion law.
