We report the first observation of the fine structure in the angular-dependent intensity of light elastically scattered by a highly transparent sample of chemical-vapor-deposition silica glass. The effect was found to be caused by small, isotropic structure defects, distributed randomly throughout the sample. The single-scattering model along with appropriate statistical theory provides the interpretation of the observed specklelike patterns with characteristic strong intensity fluctuations. The scatterer dimension was estimated to be less than 400 \AA{}.