The helix-hairpin-helix (HhH) motif is an ancient and ubiquitous nucleic acid-binding element that has emerged as a model system for studying the evolution of dsDNA-binding domains from simple peptides that phase separate with RNA. We analyzed the entire putative evolutionary trajectory of the HhH motif – from a flexible peptide to a folded domain – for functional robustness to total chiral inversion. Against expectations, functional ‘ambidexterity’ was observed for both phase separation of HhH peptides with RNA and binding of the duplicated (HhH)2-Fold to dsDNA. Moreover, dissociation kinetics, mutational analysis, and molecular dynamics simulations revealed overlap between the binding modes adopted by the natural and mirror-image proteins to natural dsDNA. The retention of several dissociation phases upon chiral inversion may reflect the history of (HhH)2-Fold binding, with the ultimate emergence of a high-affinity binding mode depopulating but not displacing more primitive (ambidextrous) modes. These data underscore the surprising functional robustness of the HhH protein family and could suggest that the veil between worlds with alternative chiral preferences may not be as impenetrable as is often assumed.