We present chemical abundances for planetary nebulae and H II regions in the Local Group dwarf irregular galaxy NGC 6822 based upon spectroscopy obtained at the Canada-France-Hawaii Telescope using the Multi-Object Spectrograph. From these and similar data compiled from the literature for planetary nebulae in the Magellanic Clouds, Sextans A, Sextans B, and Leo A, we consider the origin and evolution of the stellar progenitors of bright planetary nebulae in dwarf irregular galaxies. On average, the oxygen abundance observed in the bright planetary nebulae in these galaxies coincides with that measured in the interstellar medium, indicating that, in general, the bright planetary nebulae in dwarf irregulars descend primarily, though not exclusively, from stars formed in the relatively recent past. We also find that the ratio of neon to oxygen abundances in these bright planetary nebulae is identical to that measured in the interstellar medium, indicating that neither abundance is significantly altered as a result of the evolution of their stellar progenitors. We do find two planetary nebulae, that in Sextans A and S33 in NGC 6822, where oxygen appears to have been dredged up, but these are the exception rather than the rule. In fact, we find that even nitrogen is not always dredged up, so it appears that the dredge-up of oxygen is uncommon for the abundance range of the sample.

accepted for publication in ApJ