A simple steady-state photochemical model is developed in order to determine typical molecular oxygen concentrations for a comprehensive range of primitive abiotic atmospheres. Carbon dioxide is assumed to be the dominant constituent in these atmospheres since CO2 photodissociation may potentially result in the enhancement of the O2 partial pressure. The respective effects of the H2O content, temperature, eddy diffusion coefficient and UV flux on the results are investigated. It is shown that for any pressure at the surface, the partial pressure of molecular oxygen does not exceed 10 mbar. The peculiar case of a runaway greenhouse which has possibly taken place on Venus is qualitatively envisaged. Although O2 is basically absent in the present Venus atmosphere, a transient presence in a primitive stage cannot be ruled out. Possible mechanisms for O2 removal in such an atmosphere are reviewed. At the present stage, we think that the detection of large O2 amounts would be at least a good clue for the presence of life on an extrasolar planet.