The origin of dust in the early universe has been the subject of considerable debate. Core-collapse supernovae (ccSNe), which occur several million years after their massive progenitors form, could be a major source of that dust, as in the local universe several ccSNe have been observed to be copious dust producers. Here we report nine near-infrared (0.8-2.5{mu}m) spectra, obtained with GNIRS on Gemini North, of the Type II-P supernova (SN) 2017eaw in NGC 6946, spanning the time interval 22-205 days after discovery. The spectra show the onset of CO formation and continuum emission at wavelengths greater than 2.1{mu}m from newly formed hot dust, in addition to numerous lines of hydrogen and metals, which reveal the change in ionization as the density of much of the ejecta decreases. The observed CO masses estimated from a local thermodynamic equilibrium (LTE) model are typically 10^-4^M_{sun}_ during days 124-205, but could be an order of magnitude larger if non-LTE conditions are present in the emitting region. The timing of the appearance of CO is remarkably consistent with the chemically controlled dust models of Sarangi & Cherchneff.