We report on the formation of chiral domains self-assembled from terephthalic acid (TPA) and iron on a Cu(110) surface. Using scanning tunnelling microscopy, we observe that the supramolecular structures are organized on successive hierarchical levels. Chirality develops only at the latest assembly step, with the primary TPA constituents and the secondary diiron-terephthalate metal-organic complexes being mirror symmetric. The driving forces for the generation of these high-order chiral architectures are identified as competing coordination bonding within the metal-organic complexes and hydrogen bonding among them. The emergence of extended metal-organic networks is hindered by the incommensurability with the substrate.