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The chemical abundances of spiral galaxies, as probed by HII regions across their disks, are key to understanding the evolution of galaxies over a wide range of environments. We present LBT/MODS spectra of 52 HII regions in NGC3184 as part of the CHemical Abundances Of Spirals (CHAOS) project. We explore the direct-method gas-phase abundance trends for the first four CHAOS galaxies, using temperature measurements from one or more auroral line detections in 190 individual HII regions. We find the dispersion in Te-Te relationships is dependent on ionization, as characterized by F_5007/F_3727, and so recommend ionization-based temperature priorities for abundance calculations. We confirm our previous results that [NII] and [SIII] provide the most robust measures of electron temperature in low-ionization zones, while [OIII] provides reliable electron temperatures in high-ionization nebula. We measure relative and absolute abundances for O, N, S, Ar, and Ne. The four CHAOS galaxies marginally conform with a universal O/H gradient, as found by empirical IFU studies when plotted relative to effective radius. However, after adjusting for vertical offsets, we find a tight universal N/O gradient of alpha_N/O = -0.33 dex/Re with sigma_tot. = 0.08 for Rg/Re < 2.0, where N is dominated by secondary production. Despite this tight universal N/O gradient, the scatter in the N/O-O/H relationship is significant. Interestingly, the scatter is similar when N/O is plotted relative to O/H or S/H. The observable ionic states of S probe lower ionization and excitation energies than O, which might be more appropriate for characterizing abundances in metal-rich HII regions.