We use a 0.040 < z < 0.085 sample of 37866 star-forming galaxies from the Fourth Data Release of the Sloan Digital Sky Survey to investigate the dependence of gas-phase chemical properties on stellar mass and environment. The local density, determined from the projected distances to the fourth and fifth nearest neighbours, is used as an environment indicator. Considering environments ranging from voids, i.e., log Sigma < -0.8, to the periphery of galaxy clusters, i.e., log Sigma =~ 0.8, we find no dependence of the relationship between galaxy stellar mass and gas-phase oxygen abundance, along with its associated scatter, on local galaxy density. However, the star-forming gas in galaxies shows a marginal increase in the chemical enrichment level at a fixed stellar mass in denser environments. Compared with galaxies of similar stellar mass in low density environments, they are enhanced by a few per cent for massive galaxies to about 20 per cent for galaxies with stellar masses < 10^{9.5} solar masses. These results imply that the evolution of star-forming galaxies is driven primarily by their intrinsic properties and is largely independent of their environment over a large range of local galaxy density.