We have designed and built a four-mirror grazing incidence, illumination system for extreme ultraviolet lithography that is applicable to a two-aspherical-mirror reduction system. It was designed for a synchrotron radiation source, acid it provides uniform illumination (size : 100 x 125 mm) and proper numerical aperture for incoherent illumination of the demagnifying optics. A large illumination area was achieved by an oscillating mirror and synchronous movement of the mask and wafer stages. Experimental results have demonstrated that, with a reduction ratio of 1/5, this system is capable of replicating chips of practical size (20 x 25 mm).