The chemical abundances of the nearby spiral galaxy M33 have been the focus of numerous prior studies. In many cases, the abundance gradient determined for M33 has been limited by the wavelength coverage of the detector used for observation, the number of H II regions observed, or the amount of high-quality auroral line detections. To discern the chemical abundance gradient and the dispersion about the gradient, the CHemical Abundances Of Spirals (CHAOS) project has observed nearly 100 bright H II regions across the disk of M33. We use the Multi-Object Double Spectrograph (MODS) on the Large Binocular Telescope (LBT) to detect multiple temperature-sensitive auroral lines at high signal-to-noise in each region. Additionally, long-slit spectra are obtained for the largest and most extended H II structures, allowing for accurate direct abundance calculations out to 7.3 kpc from the galactic center. The electron temperatures are used to create a homogeneous sample of Te-Te relations that are compared to those from the literature and to those established using the present CHAOS sample of direct temperatures. The direct oxygen abundance gradient is determined and the scatter about the gradient is assessed in relation to previous direct abundance studies of the galaxy.