In this work we present new data that sets strong constraints on the solar oxygen abundance. Our approach, based on the analysis of spectropolarimetric observations, is almost model-independent and therefore extremely robust. The asymmetry of the Stokes V profile of the 6300 Å [O I] and Ni I blend is used as an indicator of the relative abundances of these two elements. The peculiar shape of the profile requires a value of ɛO = 730 +/- 100 ppm (parts per million), or logɛO = 8.86 +/- 0.07 in the logarithmic scale commonly used in astrophysics. The uncertainty range includes the model dependence as well as uncertainties in the oscillator strengths of the lines. We emphasize that the very low degree of model dependence in our analysis makes it very reliable compared to traditional determinations.