To test the existence of a possible radial gradient in oxygen abundances within the Local Group dwarf irregular galaxy NGC 6822, we have obtained optical spectra of 19 nebulae with the EFOSC2 spectrograph on the 3.6-m telescope at ESO La Silla. The extent of the measured nebulae spans galactocentric radii in the range between 0.05 kpc and 2 kpc (over four exponential scale lengths). In five H II regions (Hubble I, Hubble V, Kα, Kβ, KD 28e), the temperature-sensitive [O III] λ4363 emission line was detected, and direct oxygen abundances were derived. Oxygen abundances for the remaining H II regions were derived using bright-line methods. The oxygen abundances for three A-type supergiant stars are slightly higher than nebular values at comparable radii. Linear least-square fits to various subsets of abundance data were obtained. When all of the measured nebulae are included, no clear signature is found for an abundance gradient. A fit to only newly observed H II regions with [O III] λ4363 detections yields an oxygen abundance gradient of −0.14 ± 0.07 dex kpc −1 . The gradient becomes slightly more significant (−0.16 ± 0.05 dex kpc −1 ) when three additional H II regions with [O III] λ4363 measurements from the literature are added. Assuming no abundance gradient, we derive a mean nebular oxygen abundance 12+log(O/H) = 8.11 ± 0.10 from [O III] λ4363 detections in the five H II regions from our present data; this mean value corresponds to [O/H] = −0.55. 3.1.1. Oxygen Abundances: [O III] λ4363 Temperatures The "direct" conversion of emission-line intensities into ionic abundances requires a reliable estimate of the electron temperature of the ionized gas. We adopt a two-zone model for H II regions, with a low-and a high-ionization zone characterized by temperatures T e (O + ) and T e (O +2 ), respectively. The temperature in the O +2 zone is measured with the emission-line ratio I([O III] λ5007)/I([O III] λ4363) (Os terbrock 1989). The temperature in the O + zone is given bywhere t e = T e /10 4 K (Campbell et al. 1986;Garnett 1992). The total oxygen abundance by number is given by O/H = O + /H + + O +2 /H + . For conditions found in typical H II regions and those presented here, very little oxygen in neutral form is expected, and in the absence of He II emission, the O +3 contribution is considered negligible. For subsequent calculations of ionic abundances, we assume the following electron temperatures for specific ions (Garnett 1992;Thuan et al. 1995):, t e (Ar +2 ) = 0.83 t e (O +2 ) + 0.17, and t e (Ar +3 ) = t e (O +2 ).Derived ionic and total abundances are listed in Tables 6a and 6b, which include derived O + and O +2 electron temperatures, O + and O +2 ionic abundances, and the total oxygen abundances. Direct H II region oxygen abundances were derived for Hubble I, Hubble V, Kα, Kβ, and KD 28e, and were in excellent agreement with those derived from the method described by Skillman et al. (2003).Where [S II] λλ4068,4076 and [O II] λλ7320,7330 were detected in the spectra for Hubble V, Kα, and KD 28e, we used ...