We present a catalog of optical and infrared identifications (ID) of X-ray sources in the {AKARI} North Ecliptic Pole (NEP) Deep field detected with Chandra covering ~0.34deg^2^ with 0.5-2keV flux limits ranging ~2-20*10^-16^erg/s/cm^2^. The optical/near-infrared counterparts of the X-ray sources are taken from our Hyper Suprime Cam (HSC)/Subaru and Wide-Field InfraRed Camera (WIRCam)/Canada-France-Hawaii Telescope (CFHT) data because these have much more accurate source positions due to their spatial resolution than that of Chandra and longer wavelength infrared data. We concentrate our identifications in the HSC g band and WIRCam Ks band-based catalogs. To select the best counterpart, we utilize a novel extension of the likelihood-ratio (LR) analysis, where we use the X-ray flux as well as g-Ks colors to calculate the likelihood ratio. Spectroscopic and photometric redshifts of the counterparts are summarized. Also, simple X-ray spectroscopy is made on the sources with sufficient source counts. We present the resulting catalog in an electronic form. The main ID catalog contains 403 X-ray sources and includes X-ray fluxes, luminosities, g and Ks band magnitudes, redshifts and their sources, optical spectroscopic properties, as well as intrinsic absorption column densities and power-law indices from simple X-ray spectroscopy. The identified X-ray sources include 27 Milky-Way objects, 57 type I AGNs, 131 other AGNs, and 15 galaxies. The catalog serves as a basis for further investigations of the properties of the X-ray and near-infrared sources in this field. We present a catalog of optical g band and near-infrared (Ks band identifications of Chandra X-ray sources in the AKARI NEP Deep field with available optical/near-infrared spectroscopic features and redshifts as well as the results of simple X-ray spectroscopy. During the process, we develop a novel X-ray flux-dependent likelihood-ratio analysis for selecting the most likely counterparts among candidates.