We compare the detailed distributions of H I, H alpha , and 150 nm far-UV (FUV) continuum emission in the spiral arms of M81 at a resolution of 9" (linear resolution 150 pc at 3.7 Mpc distance). The bright H alpha emission peaks are always associated with peaks in the FUV emission. The converse is not always true; there are many regions of FUV emission with little corresponding H alpha . The H I and the FUV are always closely associated, in the sense that the H I is often brightest around the edges of the FUV emission. The effects of extinction on the morphology are small, even in the FUV. Extensive FUV emission, often with little corresponding H alpha , indicates the presence of many "B stars," which produce mostly nonionizing UV photons. These FUV photons dissociate a small fraction of an extensive layer of H2 into H I. The observed morphology can be understood if "chimneys" are common in the spiral arms of M81, where holes are blown out of the galactic disk, exposing the bright H II regions and the corresponding FUV associated with vigorous star formation. These "naked" star-forming regions show little obscuration. H2 is turned into H I by UV photons impinging on the interior surfaces of these chimneys. The intensity of the FUV radiation measured by the Ultraviolet Imaging Telescope can dissociate the underlying H2 with a typical density of ~10 H nuclei cm-3 to produce the observed amount of H I in the spiral arms of M81. Except for thin surface layers locally heated in these photodissociation regions that are close to the FUV sources, the bulk of the molecular gas in the inner disk of M81 is apparently too cold to produce much 12CO(1--0) emission.