From seashells to DNA, chirality is expressed at every level of biological structures. In self-assembled structures it may emerge cooperatively from chirality at the molecular scale. Amphiphilic molecules, for example, can form a variety of aggregates and mesophases that express the chirality of their constituent molecules at a supramolecular scale of micrometres. Quantitative prediction of the large-scale chirality based on that at the molecular scale remains a largely unsolved problem. Furthermore, experimental control over the expression of chirality at the supramolecular level is difficult to achieve: mixing of different enantiomers usually results in phase separation. Here we present an experimental and theoretical description of a system in which chirality can be varied continuously and controllably ('tuned') in micrometre-scale structures. We observe the formation of twisted ribbons consisting of bilayers of gemini surfactants (two surfactant molecules covalently linked at their charged head groups). We find that the degree of twist and the pitch of the ribbons can be tuned by the introduction of opposite-handed chiral counterions in various proportions. This degree of control might be of practical value; for example, in the use of the helical structures as templates for helical crystallization of macromolecules.