Any time-harmonic electromagnetic wave can be uniquely decomposed into a left and a right circularly polarized component. The concept of electromagnetic chirality (em-chirality) describes differences in the interaction of these two components with a scattering object or medium. Such differences can be quantified by means of em-chirality measures. These measures attain their minimal value zero for em-achiral objects or media that interact essentially in the same way with left and right circularly polarized waves. Scattering objects or media with positive em-chirality measure interact qualitatively different with left and right circularly polarized waves, and maximally em-chiral scattering objects or media would not interact with fields of either positive or negative helicity at all. This paper examines a shape optimization problem, where the goal is to determine thin tubular structures consisting of dielectric isotropic materials that exhibit large measures of em-chirality at a given frequency. We develop a gradient based optimization scheme that uses an asymptotic representation formula for scattered waves due to thin tubular scattering objects. ... mehrNumerical examples suggest that thin helical structures are at least locally optimal among this class of scattering objects.