Magnetic domains at the surface of a ferroelectric monodomain BiFeO(3) single crystal have been imaged by hard x-ray magnetic scattering. Magnetic domains up to several hundred microns in size have been observed, corresponding to cycloidal modulations of the magnetization along the wave vector k=(δ,δ,0) and symmetry equivalent directions. The rotation direction of the magnetization in all magnetic domains, determined by diffraction of circularly polarized light, was found to be unique and in agreement with predictions of a combined approach based on a spin-model complemented by relativistic density-functional simulations. Imaging of the surface shows that the largest adjacent domains display a 120° vortex structure.