The main goal of this contribution is to show that periodic arrangements of chiral scatterers can be the basis for the development of three dimensional and isotropic negative refractive index artificial media. Three dimensionality and isotropy are key issues in this context since only three dimensional structures can be properly viewed as a ``medium,'' and only in isotropic media the refractive index is unambiguously defined. The proposed arrangements are cubic lattices of chiral split ring resonators conveniently designed to yield an isotropic behavior. The reported structures are shown to provide a significant frequency band of negative refraction with good matching to free space.