We demonstrate a prototype of a Focused Ion Beam machine based on the ionization of a laser-cooled cesium beam adapted for imaging and modifying different surfaces in the few-tens nanometer range. Efficient atomic ionization is obtained by laser promoting ground-state atoms into a target excited Rydberg state, then field-ionizing them in an electric field gradient. The method allows obtaining ion currents up to 130 pA. Comparison with the standard direct photo-ionization of the atomic beam shows, in our conditions, a 40-times larger ion yield. Preliminary imaging results at ion energies in the 1-5 keV range are obtained with a resolution around 40 nm, in the present version of the prototype. Our ion beam is expected to be extremely monochromatic, with an energy spread of the order of 1 eV, offering great prospects for lithography, imaging and surface analysis.