Translation of chirality and asymmetry across structural motifs and length scales plays a fundamental role in nature, enabling unique functionalities in contexts ranging from biological systems to synthetic materials. Here, we introduce a structural chirality transfer across the organic-inorganic interface in two-dimensional hybrid perovskites using appropriate chiral organic cations. The preferred molecular configuration of the chiral spacer cations, R-(+)- or S-(-)-1-(1-naphthyl)ethylammonium and their asymmetric hydrogen-bonding interactions with lead bromide-based layers cause symmetry-breaking helical distortions in the inorganic layers, otherwise absent when employing a racemic mixture of organic spacers. First-principles modeling predicts a substantial bulk Rashba-Dresselhaus spin-splitting in the inorganic-derived conduction band with opposite spin textures between R- and S-hybrids due to the broken inversion symmetry and strong spin-orbit coupling. The ability to break symmetry using chirality transfer from one structural unit to another provides a synthetic design paradigm for emergent properties, including Rashba-Dresselhaus spin-polarization for hybrid perovskite spintronics and related applications.