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 , K \alpha , K \beta , KD 28e ) , the temperature-sensitive [ O iii ] \lambda 4363 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 ] \lambda 4363 detections yields an oxygen abundance gradient of -0.14 \pm 0.07 dex kpc ^ { -1 } . The gradient becomes slightly more significant ( -0.16 \pm 0.05 dex kpc ^ { -1 } ) when three additional H II regions with [ O iii ] \lambda 4363 measurements from the literature are added . Assuming no abundance gradient , we derive a mean nebular oxygen abundance 12 + log ( O/H ) = 8.11 \pm 0.10 from [ O iii ] \lambda 4363 detections in the five H II regions from our present data ; this mean value corresponds to [ O/H ] = -0.55 .