We present a \sim 1 \arcsec ( 100 pc ) resolution ^ { 12 } CO ( 3–2 ) map of the nearby intermediate stage interacting galaxy pair NGC 4038/9 ( the Antennae galaxies ) obtained with the Submillimeter Array . We find that half the CO ( 3–2 ) emission originates in the overlap region where most of the tidally induced star formation had been previously found in shorter wavelength images , with the rest being centered on each of the nuclei . The gross distribution is consistent with lower resolution single dish images , but we show for the first time the detailed distribution of the warm and dense molecular gas across this galaxy pair at resolutions comparable to the size of a typical giant molecular complex . While we find that 58 % ( 33/57 ) of the spatially resolved Giant Molecular Associations ( GMAs ; a few \times 100 pc ) are located in the overlap region , only \leq 30 \% spatially coincides with the optically detected star clusters , suggesting that the bulk of the CO ( 3–2 ) emission traces the regions with very recent or near future star formation activity . The spatial distribution of the CO ( 3–2 ) /CO ( 1–0 ) integrated brightness temperature ratios mainly range between 0.3 and 0.8 , which suggests that on average the CO ( 3–2 ) line in the Antennae is not completely thermalized and similar to the average values of nearby spirals . A higher ratio is seen in both nuclei and the southern complexes in the overlap region . Higher radiation field associated with intense star formation can account for the nucleus of NGC 4038 and the overlap region , but the nuclear region of NGC 4039 show relatively little star formation or AGN activities and can not be easily explained . We show kinematical evidence that the high line ratio in NGC 4039 is possibly caused by gas inflow into the counter-rotating central disk .