Increasing the sensitivity of chiral spectroscopic techniques such as circular dichroism (CD) spectroscopy is a current aspiration in the research field of nanophotonics. Enhancing CD spectroscopy depends on two complementary requirements: the enhancement of the electromagnetic fields perceived by the molecules under study and the conservation of the helicity of those fields, guaranteed by duality symmetry. In this work, we introduce a systematic method to design nanostructured dual periodic photonic systems capable of enhancing molecular CD spectroscopy resonantly. As an illustration, we engineer a dual 1D silicon nanoparticle array and show that its collective optical modes can be efficiently employed to resonantly enhance by 2 orders of magnitude the local density of optical chirality and, thus, the CD signal obtained from a given molecular sample on its vicinity.