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We mapped the 145 $\mu$m [O~I] and 158~$\mu$m [C~II] fine-structure lines in a 6$'$ $\times$ 6$'$ (4 $\times$ 4 pc) region of the W3 Main molecular cloud. The lines were mapped at 55$"$ resolution using the MPE Far-Infrared Fabry-Perot array spectrometer on board the NASA Kuiper Airborne Observatory. The lines arise in dense, photodissociated gas on the surfaces of clumps illuminated by UV photons escaping from embedded compact H~II regions. Comparison of the [O~I] and [C~II] maps with a $^{13}$CO J=2$\rightarrow$1 line map of the same region observed at the Caltech Submillimeter Observatory shows that the [O~I] emission is confined to the region with the highest column-density of molecular gas. The [C~II] emission, however, arises not only in the densest part of the molecular cloud, but also south of the molecular core where the molecular gas has been almost completely photodissociated by young O and B stars. In the molecular core, the distribution of [O~I] and [C~II] emission is quite similar, suggesting that the lines arise in the same gas. The peaks of the [O~I] and [C~II] emission both occur just south of the W3(A) H~II region. The [O~I] map also show several secondary emission peaks adjacent to W3(B) and W3(D). The [O~I]/[C~II] intensity ratio varies from 0.1 at the cloud edge to about 1 near W3(B). Comparison of this ratio and the absolut intensity of the [O~I] emission with photodissociation region models (e.g. Burton, Hollenbach, and Tielens 1990) indicates that the gas densities range from 10$^4$ to 10$^6$ cm$^{-3}$ in the cloud core.