The CHemical Abundances of Spirals ( CHAOS ) project leverages the combined power of the Large Binocular Telescope ( LBT ) with the broad spectral range and sensitivity of the Multi Object Double Spectrograph ( MODS ) to measure “ direct ” abundances ( based on observations of the temperature-sensitive auroral lines ) in large samples of H ii regions in spiral galaxies . We present LBT MODS observations of 62 H ii regions in the nearby spiral galaxy NGC 628 , with an unprecedentedly large number of auroral lines measurements ( 18 [ O iii ] \lambda 4363 , 29 [ N ii ] \lambda 5755 , 40 [ S iii ] \lambda 6312 , and 40 [ O ii ] \lambda \lambda 7320 , 7330 detections ) in 45 H ii regions . Comparing derived temperatures from multiple auroral line measurements , we find : ( 1 ) a strong correlation between temperatures based on [ S iii ] \lambda 6312 and [ N ii ] \lambda 5755 ; and ( 2 ) large discrepancies for some temperatures based on [ O ii ] \lambda \lambda 7320 , 7330 and [ O iii ] \lambda 4363 . Both of these trends are consistent with other observations in the literature , yet , given the widespread use and acceptance of [ O iii ] \lambda 4363 as a temperature determinant , the magnitude of the T [ O iii ] discrepancies still came as a surprise . Based on these results , we conduct a uniform abundance analysis prioritizing the temperatures derived from [ S iii ] \lambda 6312 and [ N ii ] \lambda 5755 , and report the gas-phase abundance gradients for NGC 628 . Relative abundances of S/O , Ne/O , and Ar/O are constant across the galaxy , consistent with no systematic change in the upper IMF over the sampled range in metallicity . These alpha-element ratios , along with N/O , all show small dispersions ( \sigma \sim 0.1 dex ) over 70 % of the azimuthally averaged radius . We interpret these results as an indication that , at a given radius , the interstellar medium in NGC 628 is chemically well-mixed . Unlike the gradients in the nearly temperature-independent relative abundances , O/H abundances have a larger intrinsic dispersion of \sim 0.165 dex . We posit that this dispersion represents an upper limit to the true dispersion in O/H at a given radius and that some of that dispersion is due to systematic uncertainties arising from temperature measurements .