  The CHemical Abundances of Spirals (CHAOS) project leverages the combined
power of the Large Binocular Telescope with the broad spectral range and
sensitivity of the Multi Object Double Spectrograph (MODS) to measure direct
abundances in large samples of HII regions in spiral galaxies. We present LBT
MODS observations of 109 Hii regions in NGC5457, of which 74 have robust
measurements of key auroral lines, a factor of 3 larger than all previous
published detections of auroral lines in the HII regions of NGC5457. Comparing
the temperatures derived from the different ionic species we find: (1) strong
correlations of T[NII] with T[SIII] and T[OIII], consistent with little or no
intrinsic scatter; (2) a correlation of T[SIII] with T[OIII], but with
significant intrinsic dispersion; (3) overall agreement between T[NII], T[SII],
and T[OII], as expected, but with significant outliers; (4) the correlations of
T[NII] with T[SIII] and T[OIII] match the predictions of photoionization
modeling while the correlation of T[SIII] with T[OIII] is offset from the
prediction of photoionization modeling. Based on these observations, which
include significantly more observations of lower excitation HII 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 HII 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 in O/H and 0.095 in N/O (at a given
radius). We stress that this measurement of the intrinsic dispersion comes
exclusively from direct measurements of HII regions in NGC5457.
