The fabrication of ordered arrays of exchange biased Ni/FeF(2) nanostructures by focused ion beam lithography is reported. High quality nano-elements, with controlled removal depth and no significant re-deposition, were carved using small ion beam currents (30 pA), moderate dwell times (1 micros) and repeated passages over the same area. Two types of nanostructures were fabricated: square arrays of circular dots with diameters from 125 +/- 8 to 500 +/- 12 nm and periodicities ranging from 200 +/- 8 to 1000 +/- 12 nm, and square arrays of square antidots (207 +/- 8 nm in edge length) with periodicities ranging from 300 +/- 8 to 1200 +/- 12 nm. The arrays were characterized using scanning ion and electron microscopy, and atomic force microscopy. The effect of the patterning on the exchange bias field (i.e., the shift in the hysteresis loop of ferromagnetic Ni due to proximity to antiferromagnetic FeF(2)) was studied using magneto-transport measurements. These high quality nanostructures offer a unique method to address some of the open questions regarding the microscopic origin of exchange bias. This is not only of major relevance in the fabrication and miniaturization of magnetic devices but it is also one of the important proximity phenomena in nanoscience and materials science.