Carbon nanothreads are a new type of one-dimensional sp(3)-carbon nanomaterial formed by slow compression and decompression of benzene. We report characterization of the chemical structure of C-13-enriched nanothreads by advanced quantitative, selective, and two-dimensional solid-state nuclear magnetic resonance (NMR) experiments complemented by infrared (IR) spectroscopy. The width of the NMR spectral peaks suggests that the nanothread reaction products are much more organized than amorphous carbon. In addition, there is no evidence from NMR of a second phase such as amorphous mixed sp(2)/sp(3)-carbon. Spectral editing reveals that almost all carbon atoms are bonded to one hydrogen atom, unlike in amorphous carbon but as is expected for enumerated nanothread structures. Characterization of the local bonding structure confirms the presence of pure fully saturated "degree-6" carbon nanothreads previously deduced on the basis of crystal packing considerations from diffraction and transmission electron microscopy. These fully saturated threads comprise between 20% and 45% of the sample. Furthermore, C-13-C-13 spin exchange experiments indicate that the length of the fully saturated regions of the threads exceeds 2.5 nm. Two-dimensional C-13-C-13 NMR spectra showing bonding between chemically nonequivalent sites rule out enumerated single-site thread structures such as polytwistane or tube (3,0) but are consistent with multisite degree-6 nanothreads. Approximately a third of the carbon is in "degree-4" nanothreads with isolated double bonds. The presence of doubly unsaturated degree-2 benzene polymers can be ruled out on the basis of C-13-C-13 NMR with spin exchange rate constants tuned by rotational resonance and H-1 decoupling. A small fraction of the sample consists of aromatic rings within the threads that link sections with mostly saturated bonding. NMR provides the detailed bonding information necessary to refine solid-state organic synthesis techniques to produce pure degree-6 or degree-4 carbon nanothreads.