  We have studied the dielectric properties of the ferromagnetic spinel
CdCr$_2$S$_4$ from first principles. Zone-center phonons and Born effective
charges were calculated by frozen-phonon and Berry phase techniques within
LSDA+U. We find that all infrared-active phonons are quite stable within the
cubic space group. The calculated static dielectric constant agrees well with
previous measurements. These results suggest that the recently observed
anomalous dielectric behavior in CdCr$_2$S$_4$ is not due to the softening of a
polar mode. We suggest further experiments to clarify this point.
