The Chandra COSMOS Survey (C-COSMOS) is a large, 1.8 Ms, Chandra program that has imaged the central 0.9 deg2 of the COSMOS field down to limiting depths of 1.9 × 10-16 erg cm-2 s-1 in the soft (0.5-2 keV) band, 7.3 × 10-16 erg cm-2 s-1 in the hard (2-10 keV) band, and 5.7 × 10-16 erg cm-2 s-1 in the full (0.5-10 keV) band. In this paper we report the i, K, and 3.6 μm identifications of the 1761 X-ray point sources. We use the likelihood ratio technique to derive the association of optical/infrared counterparts for 97% of the X-ray sources. For most of the remaining 3%, the presence of multiple counterparts or the faintness of the possible counterpart prevented a unique association. For only 10 X-ray sources we were not able to associate a counterpart, mostly due to the presence of a very bright field source close by. Only two sources are truly empty fields. The full catalog, including spectroscopic and photometric redshifts and classification described here in detail, is available online. Making use of the large number of X-ray sources, we update the "classic locus" of active galactic nuclei (AGNs) defined 20 years ago in soft X-ray surveys and define a new locus containing 90% of the AGNs in the survey with full-band luminosity >1042 erg s-1. We present the linear fit between the total i-band magnitude and the X-ray flux in the soft and hard bands, drawn over two orders of magnitude in X-ray flux, obtained using the combined C-COSMOS and XMM-COSMOS samples. We focus on the X-ray to optical flux ratio (X/O) and we test its known correlation with redshift and luminosity, and a recently introduced anti-correlation with the concentration index (C). We find a strong anti-correlation (though the dispersion is of the order of 0.5 dex) between X/O computed in the hard band and C and that 90% of the obscured AGNs in the sample with morphological information live in galaxies with regular morphology (bulgy and disky/spiral), suggesting that secular processes govern a significant fraction of the black hole growth at X-ray luminosities of 1043-1044.5 erg s-1. We also investigate the degree of obscuration of the sample using the hardness ratio, and we compare the X-ray color with the near-infrared to optical color.