Aqueous solutions of bovine A1 protein, the major component of the basic protein fraction of myelin, were studied by small angle X-ray diffraction. The experimentally determined molecular weight, 17,800, is within 3% of that corresponding to the amino acid sequence, 18, 395, and the radius of gyration was found to be 46.3 A. No equivalent scattering particle of uniform electron density could be found which was compatible with all parameters evaluated from the diffraction measurements. The possibility of a coiled shape was therefore investigated using a worm-like chain model. This yielded a contour length of 439 A and a persistence length of 15.7 A. The radius of gyration of this model chain, 47.1 A, is in quite reasonable accord with the experimental value. The latter, after correction for excluded volume effects and finite chain length, yields for the characteristic ratio, ro2/nplp-2, 5.4. This may be compared with the value, 6.1, obtained after applying a correction for finite chain length to the viscosity data given by Tanford et al. for 12 proteins in 6 M guanidine hydrochloride and 0.1 M beta-mercaptoethanol. These two experimental values fall in the expected order, since the 15% glycine content of the A1 protein is considerably higher than the average for other proteins, which is about 8%. The corresponding values predicted from conformational calculations by Miller et al. for random copolymers of the L-alanine-glycine type are 5.9 (18% glycine) and 7.0 (8% glycine). We conclude that the A1 protein exists predominately, if not exclusively, as a random coil in aqueous solution.