We present a fully sampled map covering the Orion Hot Core and dense molecular ridge, in the submillimeter J = 6-5 rotational transition of (CO)-C-13, at lambda = 0.45 mm with a resolution of 13 '' and 0.5 km s(-1). The map covers 3' by 2'. The profile centered on the Hot Core peaks at 8.5 km s(-1) and has a peak intensity of 40 K, corrected antenna temperature. It shows line wings from 30 km s(-1) to -20 km s(-1). The map of intensity, integrated from 0 to +18 km s(-1), shows a prominent maximum <5 '' from the center of the Orion Hot Core. The FWHP is 37 '' larger than the regions containing complex molecules. Single dish measurements of lines from the J = 2-1 or J = 1-0 transitions of CO isotopes show no such distinct maximum. Correcting for tau = 1.5 in the J = 6-5 line of (CO)-C-13, and assuming that the level populations are thermalized at 150 K, the beam-averaged column density between 0 to +18 km s(-1) is N((CO)-C-13) = 6.8 x 10(17) cm(-2) and N(CO) = 5.2 x 10(19) cm(-2). When combined with published dust emission data, the CO/H-2 number ratio is 2 x 10(-5), a factor of similar to 5 lower than the canonical value, 10(-4). For the Orion South and Orion Ridge region, the column density of CO is <25% of that found for the Hot Core but CO/H-2 ratios are similar. Models of photon dominated regions, PDRs, predict that CO lines from PDRs are only marginally optically thick. Thus, our map traces warm and dense molecular gas rather than PDRs.