Eleven models of Galactic chemical evolution, differing in the carbon, nitrogen,and oxygen yields adopted, have been computed to reproduce the Galactic O/H values obtained from H II regions. All the models fit the oxygen gradient, but only two models fit also the carbon gradient, those based on carbon yields that increase with metallicity due to stellar winds in massive stars (MS) and decrease with metallicity due to stellar winds in low and intermediate mass stars (LIMS). The successful models also fit the C/O versus O/H evolution history of the solar vicinity obtained from stellar observations. We also compare the present day N/H gradient and the N/O versus O/H and the C/Fe, N/Fe, O/Fe versus Fe/H evolution histories of the solar vicinity predicted by our two best models with those derived from H II regions and from stellar observations. While our two best models fit the C/H and O/H gradients as well as the C/O versus O/H history, only Model 1 fits well the N/H gradient and the N/O values for metal poor stars but fails to fit the N/H values for metal rich stars. Therefore we conclude that our two best models solve the C enrichment problem, but that further work needs to be done on the N enrichment problem. By adding the C and O production since the Sun was formed predicted by Models 1 and 2 to the observed solar values we find an excellent agreement with the O/H and C/H values of the solar vicinity derived from H II regions O and C recombination lines. One of the most important results of this paper is that the fraction of carbon due to MS and LIMS in the interstellar medium is strongly dependent on time and on the galactocentric distance; at present about half of the carbon in the interstellar medium of the solar vicinity has been produced by MS and half by LIMS. ; Comment: 34 pages, 6 tables, 7 figures. Accepted for publication in ApJ