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 x 10^-16 erg/cm²/s in the soft (0.5-2 keV) band, 7.3 x 10^-16 erg/cm²/s in the hard (2-10 keV) band, and 5.7 x 10^-16 erg/cm²/s in the full (0.5-10 keV) band. In this Paper III of the series of papers on this survey, the authors report the i, K, and 3.6-um identifications of the 1761 X-ray point sources. They 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, they 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 herein. See also the related table <a href="ccosmoscat.html">CCOSMOSCAT</a> for the the surveyed X-ray point sources. This table was created by the HEASARC in December 2012, based on the <a href="https://cdsarc.cds.unistra.fr/ftp/cats/J/ApJS/201/30">CDS Catalog J/ApJS/201/30</a> file catalog.dat. This is a service provided by NASA HEASARC .