Self-assembly of the binary molecular system of pentacene and 3,4,9,10-perylenetetracarboxylic dianhydride (PTCDA) on Ag(111) has been investigated by low-temperature scanning tunneling microscopy, molecular dynamics (MD), and density functional theory (DFT) calculations. Well-ordered two-dimensional (2D) pentacene:PTCDA supramolecular chiral networks are observed to form on Ag(111). The 2D chiral network formation is controlled by the strong interfacial interaction between adsorbed molecules and the underlying Ag(111), as revealed by MD and DFT calculations. The registry effect locks the adsorbed pentacene and PTCDA molecules into specific adsorption sites due to the corrugation of the potential energy surface. The 2D supramolecular networks are further constrained through the directional CO...H-C multiple intermolecular hydrogen bonding between the anhydride groups of PTCDA and the peripheral aromatic hydrogen atoms of the neighboring pentacene molecules.