An accurate determination of photospheric solar abundances requires detailed modeling of the solar granulation and accounting for departures from local thermodynamical equilibrium (LTE). We argue that the forbidden C I line at 8727 Å is largely immune to departures from LTE and can be realistically modeled using LTE radiative transfer in a time-dependent three-dimensional simulation of solar surface convection. We analyze the [C I] line in the solar flux spectrum to derive the abundance logɛ(C)=8.39+/-0.04 dex. Combining this result with our parallel analysis of [O I] λ6300, we find C/O=0.50+/-0.07, in agreement with the ratios measured in the solar corona from gamma-ray spectroscopy and solar energetic particles.