We report the detection of a deep 3P1 -> 3P0 [CI] absorption feature at vlsr = 12 km s-1 with a linewidth of 6 km/sec towards extended line emission at a distance of 11' from Sgr C. The 492 GHz observations were made with the Antarctic Submillimeter Telescope and Remote Observatory (AST/RO). The absorption feature allows the derivation of lower limits for the CI column density in the cold foreground material. The feature is unlikely to be caused by self-absorption within the [CI] emitting cloud because it is observed over a region at least 4' across and is also seen in emission 22' north of the Galactic plane in 12CO J=2-1. In order to determine the temperature and the abundance ratio of CI to CO in the foreground gas, we compare the observations with 12CO and 13CO J=1-0 observations obtained with the Bell Labs 7 m antenna and with 12CO and 13CO J=2-1 observations made with the KOSMA 3 m telescope. All these observations have about the same beam size. On the assumption that the background emission is not spatially associated with the absorbing cloud(s), a consistent model for the observed line intensities yields an excitation temperature of 3.5 K for 13CO and 5 K for [CI], implying low volume densities n(H_2) ~ 103 cm-3. The measured abundance ratio of CI to 13CO is ~ 34. This value is consistent with photochemical model calculations which predict an abundance ratio of CI to 12CO of ~1 and a 12CO to 13CO ratio of ~30 (reduced in comparison to the intrinsic 12C to 13C isotopic ratio of 60 by fractionation). The observed 13CO column density corresponds to an AV of 4.6m, i.e., the hydrogen column density N(H) is ~ 9 * 1021 cm-2. This, together with the observed [CI] linewidth, indicates that the absorption is likely due to several translucent clouds. We compare our results with line fluxes derived from the large-scale, low resolution COBE FIRAS spectral line survey of [CI] 3P1 -> 3P0 and [CI] 3P2 -> 3P1 emission in the galactic plane. Taking into account beam filling, the lower limit for the column density of cold (Tex <= 10 K) CI which is traced by our absorption observations is at least a factor of two higher than the column density of the warmer CI (Tex >= 20 K) detected in emission by COBE. Our results suggest that a substantial fraction of atomic carbon in the interstellar medium may be difficult to detect in [CI] emission, due to its low excitation.