The HIV-1 capsid protein (CA) forms the capsid shell that encloses RNA within a mature HIV-1 virion. Previous studies by electron microscopy have shown that the capsid shell is primarily a triangular lattice of CA hexamers, with variable curvature that destroys the ideal symmetry of a planar lattice. The mature CA lattice depends on CA dimerization, which occurs through interactions between helix 9 segments of the C-terminal domain (CTD) of CA. Several high-resolution structures of the CTD-CTD dimerization interface have been reported, based on X-ray crystallography and multidimensional solution nuclear magnetic resonance (NMR), with significant differences in amino acid side chain conformations and helix 9-helix 9 orientations. In a structural model for tubular CA assemblies based on cryogenic electron microscopy (cryoEM) [Zhao et al. Nature, 2013, 497, 643-646], the dimerization interface is substantially disordered. The dimerization interface structure in noncrystalline CA assemblies and the extent to which this interface is structurally ordered within a curved lattice have therefore been unclear. Here we describe solid state NMR measurements on the dimerization interface in tubular CA assemblies, which contain the curved triangular lattice of a mature virion, including quantitative measurements of intermolecular and intramolecular distances using dipolar recoupling techniques, solid state NMR chemical shifts, and long-range side chain-side chain contacts. When combined with restraints on the distance and orientation between helix 9 segments from the cryoEM study, the solid state NMR data lead to a unique high-resolution structure for the dimerization interface in the noncrystalline lattice of CA tubes. These results demonstrate that CA lattice curvature is not dependent on disorder or variability in the dimerization interface. This work also demonstrates the feasibility of local structure determination within large noncrystalline assemblies formed by high-molecular-weight proteins, using modern solid state NMR methods.