Chirality plays an important role in molecule recognition processes, bestowing selectivity to many life-regulating chemical reactions. Despite effort was devoted to structural studies of adsorbed molecules and supramolecular assemblies at surfaces in relation to chirality during the last decades, their electronic properties and substrate-molecule interactions require further exploration. Here we examine self-assembled nanoporous square networks formed by the linear 4,4"-diethynyl-1,1':4',1"-terphenyl tecton on Ag(100) using scanning probe microscopy and spectroscopy under ultrahigh vacuum conditions. We find that the networks are stabilized by 4-fold surface chiral bonding motifs and noncontact atomic force microscopy reveals the underlying C-H/π interaction. The chiral assembly domains are commensurate with the Ag(100) substrate and equally oriented. Using tunneling spectroscopy, a surprisingly variable symmetry of electronic structure is unveiled, which becomes distinctly achiral at high voltages and enhanced as the wave function decays into the vacuum. Close to the molecular plane, both observations and computational modeling reveals a chiral electronic structure governed by the chirality induced by the 4-fold C-H/π bonds and phenyl twisting. Far from the molecular plane, these effects attenuate and the electronic structure becomes achiral, following the square-symmetric substrate lattice. In addition, a hybrid node state develops at high energies and accounts for a chess-board electronic landscape. These insights show how self-assembled chiral lattices can be used to gently steer electronic symmetry, with potential for creating programmable textures in nanoscale materials.