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(Abridged) We have obtained new spectrophotometric data for 28 HII regions inthe spiral galaxy NGC 300, a member of the nearby Sculptor Group. The detectionof auroral lines, including [OIII]4363, [SIII]6312 and [NII]5755, has allowedus to measure electron temperatures and direct chemical abundances for thewhole sample. We determine for the first time in this galaxy a radial gas-phaseoxygen abundance gradient based solely on auroral lines, and obtain thefollowing least-square solution: 12+log(O/H)=8.57-0.41 R/R25, where thegalactocentric distance is expressed in terms of the isophotal radius R25. Thegradient corresponds to -0.077 dex/kpc, and agrees very well with thegalactocentric trend in metallicity obtained for 29 B and A supergiants in thesame galaxy. The intercept of the regression for the nebular data virtuallycoincides with the intercept obtained from the stellar data. This allows littleroom for depletion of nebular oxygen onto dust grains, although in this kind ofcomparison we are somewhat limited by systematic uncertainties, such as thoserelated to the atomic parameters used to derive the chemical compositions.  We discuss the implications of our result with regard to strong-lineabundance indicators commonly used to estimate the chemical compositions ofstar-forming galaxies, such as R23. By applying a few popular calibrations ofthese indices based on grids of photoionization models on the NGC 300 HIIregion fluxes we find metallicities that are higher by 0.3 dex (a factor oftwo) or more relative to our nebular (Te-based) and stellar ones.  We confirm a metallicity dependence of the `softness' parametereta=(O+/O++)/(S+/S++), in the sense that softer stellar continua are found athigh metallicity.

Extragalactic chemical abundances: do HII regions and young stars tell the same story? The case of the spiral galaxy NGC 300