  The dispersion in chemical abundances provides a very strong constraint on
the processes that drive the chemical enrichment of galaxies. Due to its
proximity, the spiral galaxy M33 has been the focus of numerous chemical
abundance surveys to study the chemical enrichment and dispersion in abundances
over large spatial scales. The CHemical Abundances Of Spirals (CHAOS) project
has observed $\sim$100 H II regions in M33 with the Large Binocular Telescope
(LBT), producing the largest homogeneous sample of electron temperatures
(T$_e$) and direct abundances in this galaxy. Our LBT observations produce a
robust oxygen abundance gradient of $-$0.037 $\pm$ 0.007 dex/kpc and indicate a
relatively small (0.043 $\pm$ 0.015 dex) intrinsic dispersion in oxygen
abundance relative to this gradient. The dispersions in N/H and N/O are
similarly small and the abundances of Ne, S, Cl, and Ar relative to O are
consistent with the solar ratio as expected for $\alpha$-process or
$\alpha$-process-dependent elements. Taken together, the ISM in M33 is
chemically well-mixed and homogeneously enriched from inside-out with no
evidence of significant abundance variations at a given radius in the galaxy.
Our results are compared to those of the numerous studies in the literature,
and we discuss possible contaminating sources that can inflate abundance
dispersion measurements. Importantly, if abundances are derived from a single
T$_e$ measurement and T$_e$-T$_e$ relationships are relied on for inferring the
temperature in the unmeasured ionization zone, this can lead to systematic
biases which increase the measured dispersion up to 0.11 dex.
