We report the first measurements of the absolute ionization yield of nuclear recoils in liquid xenon, as a function of energy and electric field. Independent experiments were carried out with two dual-phase time-projection chamber prototypes, developed for the XENON dark matter project. We find that the charge yield increases with decreasing recoil energy, and exhibits only a weak field dependence. These results are the first unambiguous demonstration of the capability of dual-phase xenon detectors to discriminate between electron and nuclear recoils down to 20 keV, a key requirement for a sensitive dark matter search.