We report solution structural studies on 9--16-kilobase (kb) fragments of the 30-nm chromatin fiber isolated from calf thymus nuclei. Samples were stabilized by dimethylsuberimidate cross-linking in 100 mM salt concentration to ensure retention of a compact conformation. Electron microscopy, sedimentation diffusion, light scattering, and gel electrophoresis were used to characterize materials which were fractionated by size by utilizing sucrose gradient sedimentation. Measurements reported include the translational frictional coefficient as determined by quasielastic light scattering and the rotational frictional coefficient as deduced from transient electric dichroism. These frictional properties were combined to yield 33 +/- 3 nm for the diameter of the fiber and a length of 1.5 +/- 0.1 nm per nucleosome. Assuming a superhelix pitch of 11 nm, we calculate 7.5 +/- 0.5 nucleosomes per superhelical turn. The 30-nm fiber was found to reach saturation of electric field orientation at about 10--13 kV/cm and to lack a detectable permanent dipole moment, implying no polarity of the fiber. The limiting reduced dichroism rho was found to be +0.06, intermediate between the values expected if the nucleosomal disk diameters were parallel (rho expected = -3/8) or perpendicular (rho expected +3/4) to the fiber axis. This result implies an average angle of 51 degrees between the fiber axis and the local DNA (nucleosomal) superhelix axis and rules out many of the simple models which have been proposed for the detailed structure of the 30-nm fiber.