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 109 H ii  regions in NGC 5457 ( M 101 ) , of which 74 have robust measurements of key auroral lines ( 50 [ O iii ] \lambda 4363 , 47 [ N ii ] \lambda 5755 , 59 [ S iii ] \lambda 6312 , 67 [ O ii ] \lambda \lambda 7320 , 7330 and 70 [ S ii ] \lambda 4076 at a strength of \geq 3 \sigma ) , a factor of \sim 3 larger than all previous published detections of auroral lines in the H ii  regions of NGC 5457 . Comparing the temperatures derived from the different ionic species we find : ( 1 ) strong correlations of T [ N ii ] with T [ S iii ] and T [ O iii ] , consistent with little or no intrinsic scatter ; ( 2 ) a correlation of T [ S iii ] with T [ O iii ] , but with significant intrinsic dispersion ; ( 3 ) overall agreement between T [ N ii ] , T [ S ii ] , and T [ O ii ] , as expected , but with significant outliers ; ( 4 ) the correlations of T [ N ii ] with T [ S iii ] and T [ O iii ] match the predictions of photoionization modeling while the correlation of T [ S iii ] with T [ O iii ] is offset from the prediction of photoionization modeling . Based on these observations , which include significantly more observations of lower excitation H ii  regions , missing in many analyses , we inspect the commonly used ionization correction factors ( ICFs ) for unobserved ionic species and propose new empirical ICFs for S and Ar . We have discovered an unexpected population of H ii regions with a significant offset to low values in Ne/O , which defies explanation . We derive radial gradients in O/H and N/O which agree with previous studies . Our large observational database allows us to examine the dispersion in abundances , and we find intrinsic dispersions of 0.074 \pm 0.009 in O/H and 0.095 \pm 0.009 in N/O ( at a given radius ) . We stress that this measurement of the intrinsic dispersion comes exclusively from direct measurements of H ii  regions in NGC 5457 .