The HIV-inactivating protein cyanovirin-N (CVN) exists in two forms that are pH- and solvent-dependent: a monomer which predominates at neutral pH (greater than or equal to 90%) and a symmetric domain-swapped dimer. We have investigated the orientation of the two halves of the domain-swapped dimer of CVN at neutral pH in solution using dipolar couplings measured in a neutral liquid crystalline bicelle medium. D-1(NH) dipolar couplings for the dimer were readily measured for 18 out of 101 residues, and are shown to be inconsistent with the orientation of the two halves of the dimer observed in the X-ray structure obtained from crystals grown at low pH in the presence of organic solvent. The orientation of the two halves of the domain-swapped dimer was determined by rigid body minimization, subject to the requirements of C-2 symmetry. The starting coordinates for the calculations consisted of the X-ray coordinates for the two halves (with the linker residues deleted), separated by similar to 45 Angstrom and placed in three different relative orientations. One-half of the dimer is held fixed, the other half is free to rotate and translate (6 degrees of freedom), and the alignment tensor for the dipolar couplings is free to rotate (3 degrees of freedom). The target function comprised only four terms: dipolar coupling restraints (18 x 2), distance restraints (12) to link the two halves and to prevent steric clash, a radius of gyration restraint to achieve appropriate compaction, and a quartic van der Waals repulsion term. Structures were calculated for different target values of the radius of gyration, and back-calculation of the alignment tensor and dipolar couplings on the basis of molecular shape was used to filter the resulting structures, Prediction of dipolar couplings in this manner is predicated on the assumption that orientational order is dictated by steric interactions between the liquid crystalline medium and the protein. The validity of this assumption in this particular case is evidenced by the excellent agreement between predicted and observed dipolar couplings for the monomer. We show that the data is only consistent with a very small range of orientations of the two halves of the dimer in which the angle between the long axes of the two halves is similar to 110 degrees. The relative orientation of the two halves of the dimer at neutral pH in solution is quite different from that observed in the crystals obtained at low pH in organic solvent. The factors stabilizing the relative orientation of the two halves of the dimer under different conditions are discussed. The methodology presented in this paper should find a wide range of applicability to numerous other structural problems involving multimeric proteins and protein-protein complexes.