We report the direct abundances for the galaxy NGC 2403 as observed by the CHemical Abundances Of Spirals (CHAOS) project. Using the Multi-Object Double Spectrograph on the Large Binocular Telescope, we observe two fields with H II regions that cover an R$_g$/R$_e$ range of 0.18 to 2.31. 32 H II regions contain at least one auroral line detection, and we detect a total of 122 temperature-sensitive auroral lines. Here, for the first time, we use the intrinsic scatter in the T$_e$-T$_e$ diagrams, added in quadrature to the uncertainty on the measured temperature, to determine the uncertainty on an electron temperature inferred for one ionization zone from a measurement in a different ionization zone. We then use all available temperature data within an H II region to obtain a weighted average temperature within each ionization zone. We re-derive the oxygen abundances of all CHAOS galaxies using this new temperature prioritization method, and we find that the gradients are consistent with the results of Berg et al. (2020). For NGC 2403, we measure a direct oxygen abundance gradient of -0.09($pm$0.03) dex/Re, with an intrinsic dispersion of 0.037($pm$0.017) dex, and an N/O abundance gradient of -0.17($pm$0.03) dex/Re with an intrinsic dispersion of 0.060($pm$0.018) dex. For direct comparison, we use the line intensities from the study of NGC 2403 by Berg et al. (2013), and find their recomputed values for the O/H and N/O gradients are consistent with ours.
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