The combined effects of interstellar dust absorption and of scattering by hydrogen atoms may give rise to a Ly alpha spectral feature of negative equivalent width, as has been observed in several star-forming galaxies. By considering the transfer of Ly alpha line radiation and of neighboring stellar continuum radiation within a dusty galaxy, we find that dust absorption has three effects: (1) it reduces the apparent ultraviolet continuum luminosity at all wavelengths; (2) it preferentially decreases the apparent Ly alpha line luminosity from H II regions; and (3) it creates an ''attenuation feature'' in the continuum spectrum-centered at the Ly alpha rest frequency-which occurs because the attenuation of the stellar continuum radiation increases as the Ly alpha rest frequency is approached, due to the effects of scattering by hydrogen atoms. For plausible values of the galactic dust content and of the disk thickness, these effects can lead to a negative net Ly alpha equivalent width, even for galaxies in which the unattenuated spectrum would show a strong Ly alpha emission line.