Resonant magnetic x-ray scattering near the vanadium L-2,L-3-absorption edges has been used to investigate the low temperature magnetic structure of high quality BaVS3 single crystals. Below T-N = 31 K, the strong resonance revealed a triple-incommensurate magnetic ordering at the wave vector (0.226 0.226 xi) in hexagonal notation, with xi = 0.033. The azimuthal-angle dependence of the scattering signal and time-dependent density functional theory simulations indicate an antiferromagnetic order within the ab plane with the spins polarized along a in the monoclinic structure.