Small-angle X-ray scattering (SAXS) measurements were made on low ionic strength NaCl solutions containing 2-10 mg/mL short (150 base pairs) or long (2-22 kilobase pairs) DNA fragments in the semidilute regime. Whereas current theories of the scattering of polyelectrolytes predict a single peak in the scattering pattern in the absence of salt there is a clear interference corresponding essentially to the 20-30 nm center-to-center separation between overall isotropically distributed rigid DNA segments. Electric field X-ray scattering measurements indicate that these segments orient parallel to the electric field and that the relaxation times are identical to those of the birefringence signal.