  The CHAOS project is building a large database of LBT H II region spectra in
nearby spiral galaxies to use direct abundances to better determine the
dispersion in metallicity as a function of galactic radius. Here, we present
CHAOS LBT observations of C II $\lambda$4267 emission detected in 10 H II
regions in M 101, and, using a new photoionization model based ionization
correction factor, we convert these measurements into total carbon abundances.
A comparison with M101 C II recombination line observations from the literature
shows excellent agreement, and we measure a relatively steep gradient in
log(C/H) of -0.37 +/- 0.06 dex/R_e. The C/N observations are consistent with a
constant value of log(C/N) = 0.84 with a dispersion of only 0.09 dex, which,
given the different nucleosynthetic sources of C and N, is challenging to
understand. We also note that when plotting N/O versus O/H, all of the H II
regions with detections of CII $\lambda$4267 present N/O abundances at the
minimum of the scatter in N/O at a given value of O/H. If the high surface
brightness necessary for the detection of the faint recombination lines is
interpreted as an indicator of H II region youth, then this may point to a lack
of nitrogen pollution in the youngest H II regions. In the future, we
anticipate that the CHAOS project will significantly increase the total number
of C II $\lambda$4267 measurements in extragalactic H II regions.
