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The Orion Bright Bar is a nearby example of an edge-on Photodissociation Region (PDR), in which molecular gas is being illuminated by the intense UV flux from the Trapezium cluster. We have observed this region with the Hat Creek mm-wave interferometer in the CO and $^{13}$CO J=1$\rightarrow$0 lines, as well as in the HCO$^+$ J=1$\rightarrow$0 line. Because of the extended nature of the CO emission, we have combined the images obtained by the interferometer with single-dish observations, in order to obtain high-angular resolution maps with no missing flux; the synthesized angular resolution of the combined maps is $\sim$6-10 arcseconds. In addition to these tracers of the molecular morphology of this region, we present observations of the 609$\mu$ fine structure line of neutral atomic carbon, which traces the interface between the ionized (C$^+$) medium and the molecular material. These observations were obtained at the CalTech Submillimeter Observatory with an angular resolution of $\sim$15 arcseconds. Our observations indicate that this PDR is well described as a homogeneously distributed slab of moderately dense material ($\sim$5$\times$10$^4$ cm$^{-3}$), in which are embedded a small number of dense ($>$10$^6$ cm$^{-3}$) clumps. The latter play little or no role in determining the thickness and kinetic temperature structure of this PDR, in marked contrast to other well-known PDRS such as M17SW. The observational picture is largely supported by PDR model calculations for this region, which also account well for the intensities of a variety of other previously observed atomic and molecular emission lines.
