We present a coarsely-sampled map of the region |l|<=2^o, |b|<= 0.1^o in the 492 GHz (3P_1->3P_0) fine structure transition of neutral carbon, observed with the Antarctic Submillimeter Telescope and Remote Observatory (AST/RO). The distribution of [\ionC1] emission is similar on the large scale to that of CO J=1->0. On average, the ratio of the integrated intensities, I_[C I]/I_12CO, is higher in the Galactic disk than in the Galactic Center region. This result is accounted for by the absorption of 12CO within the clouds located in the outer Galactic disk. I_[C I]/I_12CO is surprisingly uniform over the variety of environments near the Galactic Center. On average, [\ionC1] is optically thin (or as optically thin as 13CO (J=1->0)) even in the dense molecular clouds of the Galactic Center region.