We present position-velocity strip maps of the Galactic Center region in the CO J = 7 \rightarrow 6 and J = 4 \rightarrow 3 transitions observed with the Antarctic Submillimeter Telescope and Remote Observatory ( AST/RO ) located at Amundsen-Scott South Pole Station . Emission from the two rotational transitions of ^ { 12 } CO was mapped at b = 0 ^ { \circ } for 3.5 ^ { \circ } > \ell > -1.5 ^ { \circ } , on a 1 ^ { \prime } grid with a FWHM beamsize of 58 ^ { \prime \prime } at 806 GHz and 105 ^ { \prime \prime } at 461 GHz . Previous observations of CO J = 4 \rightarrow 3 ( Martin et al. , in preparation ) and [ C I ] ( Ojha et al . 2001 ) emission from this region show that these lines are distributed in a manner similar to CO J = 1 \rightarrow 0 ( Stark et al . 1987 ) ; the ( CO J = 4 \rightarrow 3 ) / ( CO J = 1 \rightarrow 0 ) line ratio map is almost featureless across the entire Galactic Center region . In contrast , the CO J = 7 \rightarrow 6 emission from the Galactic Center is strongly peaked toward the Sgr A and Sgr B molecular complexes . A Large Velocity Gradient ( LVG ) analysis shows that aside from the two special regions Sgr A and Sgr B , the photon-dominated regions within a few hundred parsecs of the Galactic Center are remarkably uniform in mean density and kinetic temperature at n = 2500 to 4000 \mathrm { cm ^ { -3 } } and T = 30 to 45 K. The ( CO J = 7 \rightarrow 6 ) / ( CO J = 4 \rightarrow 3 ) line temperature ratios near Sgr B are a factor of two higher than those observed in the nuclear region of the starburst galaxy M82 ( Mao et al . 2000 ) , while the CO ( J = 7 \rightarrow 6 ) /CO ( J = 4 \rightarrow 3 ) line temperature ratios around Sgr A are similar to M82 . The line ratio on large scales from the Galactic Center region is an order of magnitude less than that from M82 .