  We analyze resolved stellar near-infrared photometry of 21 HST fields in M31
to constrain the impact of metallicity on the formation of carbon stars.
Observations of nearby galaxies show that the carbon stars are increasingly
rare at higher metallicity. Models indicate that carbon star formation
efficiency drops due to the decrease in dredge-up efficiency in metal-rich
thermally-pulsing Asymptotic Giant Branch (TP-AGB) stars, coupled to a higher
initial abundance of oxygen. However, while models predict a metallicity
ceiling above which carbon stars cannot form, previous observations have not
yet pinpointed this limit. Our new observations reliably separate carbon stars
from M-type TP-AGB stars across 2.6-13.7 kpc of M31's metal-rich disk using HST
WFC3/IR medium-band filters. We find that the ratio of C to M stars (C/M)
decreases more rapidly than extrapolations of observations in more metal-poor
galaxies, resulting in a C/M that is too low by more than a factor of 10 in the
innermost fields and indicating a dramatic decline in C star formation
efficiency at metallicities higher than [M/H] $\approx$ -0.1 dex. The
metallicity ceiling remains undetected, but must occur at metallicities higher
than what is measured in M31's inner disk ([M/H] $\gtrsim$ +0.06 dex).
