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We present investigations on noncovalent bonding and supramolecular self-assembly of two related molecular building blocks at a noble metal surface: 4-[trans-2-(pyrid-4-yl-vinyl)]benzoic acid (PVBA) and 4-[(pyrid-4-yl-ethynyl)]benzoic acid (PEBA). These rigid, rodlike molecules comprising the same complementary moieties for hydrogen bond formation are comparable in shape and size. For PVBA, the ethenylene moiety accounts for two-dimensional (2-D) chirality upon confinement to a surface; PEBA is linear and thus 2-D achiral. Molecular films were deposited on a Ag(111) surface by organic molecular beam epitaxy and characterized by scanning tunneling microscopy. At low temperatures (around 150 K), both species form irregular networks of flat lying molecules linked via their endgroups in a diffusion-limited aggregation process. In the absence of kinetic limitations (adsorption or annealing at room temperature), hydrogen-bonded supramolecular assemblies form which are markedly different. With PVBA, enantiomorphic twin chains in two mirror-symmetric species running along a high-symmetry direction of the substrate lattice form by diastereoselective self-assembly of one enantiomer. The chirality signature is strictly correlated between neighboring twin chains. Enantiopure one-dimensional (1-D) supramolecular nanogratings with tunable periodicity evolve at intermediate coverages, reflecting chiral resolution in micrometer domains. In contrast, PEBA assembles in 2-D hydrogen-bonded islands, which are enantiomorphic because of the orientation of the supramolecular arrangements along low-symmetry directions of the substrate. Thus, for PVBA, chiral molecules form 1-D enantiomorphic supramolecular structures because of mesoscopic resolution of a 2-D chiral species, whereas with PEBA, the packing of an achiral species causes 2-D enantiomorphic arrangements. Model simulations of supramolecular ordering provide a deeper understanding of the stability of these systems.