The charge and energy resolution response of a liquid xenon ionization chamber has been measured with Bi-207 electrons and gamma-rays. The applied electric field was varied in the range 0.06-12 kV/cm. After an initial steep rise, charge collection increases slowly above a few kV/cm and does not reach saturation within our range. This field dependence has been analyzed in view of different recombination models. The best agreement is obtained by including the contribution of delta electrons. The best energy resolution, measured at 12 kV/cm, is 5.9% FWHM for gamma-rays of 570 keV. This value is consistent with the expected recombination fluctuations in the number of electron-ion pairs associated with low energy delta electron tracks.