A study of the relative abundances of the rare isotopic species H(C-12)(N-15) and H(C-13)(N-14) has been made in six dense molecular clouds through observations of the 3.5-mm rotational transitions. The data indicate that in all sources the HC(N-15)/H(C-13)N integrated line-intensity ratio is smaller than that implied by terrestrial isotopic abundances. The excitation of HCN is discussed with special attention to the conditions which permit accurate abundance determination even when optical depths are large. A quantitative estimate of the line saturation shows this to be a small effect for the present measurements. There appears to be at least a factor of 6 between the average ratio for the sources in the galactic disk and that for two sources associated with the galactic center. This result is discussed in terms of increased nuclear processing in the galactic center region.