A one-dimensional (1D) sp3 carbon nanomaterial with high lateral packing order, known as carbon nanothreads, has recently been synthesized by slowly compressing and decompressing crystalline solid benzene at high pressure. The atomic structure of an individual nanothread has not yet been determined experimentally. We have calculated the 13C nuclear magnetic resonance (NMR) chemical shifts, chemical shielding tensors, and anisotropies of several axially ordered and disordered partially saturated and fully saturated nanothreads within density functional theory and systematically compared the results with experimental solid-state NMR data to assist in identifying the structures of the synthesized nanothreads. In the fully saturated threads, every carbon atom in each progenitor benzene molecule has bonded to a neighboring molecule (i.e., 6 bonds per molecule, a so-called “degree-6” nanothread), while the partially saturated threads examined retain a single double bond per benzene ring (“degree-4”). The most-parsimonious theoretical fit to the experimental 1D solid-state NMR spectrum, constrained by the measured chemical shift anisotropies and key features of two-dimensional NMR spectra, suggests a certain combination of degree-4 and degree-6 nanothreads as plausible components of this 1D sp3 carbon nanomaterial, with intriguing hints of a [4 + 2] cycloaddition pathway toward nanothread formation from benzene columns in the progenitor molecular crystal, based on the presence of nanothreads IV-7, IV-8, and square polymer in the minimal fit.