We compare the detailed distributions of HI, H alpha, and 150 nm far-UV 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 far-UV emission. The converse is not always true; there are many regions of far-UV emission with little corresponding H alpha. The HI and the far-UV are always closely associated, in the sense that the HI is often brightest around the edges of the far-UV emission. The effects of extinction on the morphology are small, even in the far-UV. Extensive far-UV emission, often with little corresponding H alpha, indicates the presence of many ``B-stars'', which produce mostly non-ionizing UV photons. These far-UV photons dissociate a small fraction of an extensive layer of H_2 into HI. 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 HII regions and the corresponding far-UV associated with vigorous star formation. These ``naked'' star-forming regions show little obscuration. H_2 is turned into HI by UV photons impinging on the interior surfaces of these chimneys. The intensity of the far-UV radiation measured by UIT can dissociate the underlying H_2 with a typical density of ~10 H nucleii cm**-3 to produce the observed amount of HI in the spiral arms of M81. Except for thin surface layers locally heated in these photo-dissociation regions close to the far-UV sources, the bulk of the molecular gas in the inner disk of M81 is apparently too cold to produce much 12CO(1-0) emission.
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