Gamma peptide nucleic acids (PNAs) are a promising class of nucleic acid mimics that adopt either a right- or left-handed helical motif as individual strands and hybridize to DNA or RNA with high affinity and sequence specificity, or not at all, depending on the helical sense. They are attractive as antisense and antigene reagents, as well as building blocks for molecular self-assembly; however, they have not been widely adopted due to their relatively poor biophysical attributes and the challenge in chemical modifications. Here, we report the development of a set of universal monomers, four each for both the right- and left-handed conformers, that permit rapid and selective on-resin chemical functionalization and diversification. The system is modular, permitting incorporation of different chemical groups in the backbone without causing adverse effects on hybridization. The approach overcomes the need to prepare a new set of monomers each time a different chemical group is introduced in the backbone. The newly added synthetic flexibility, along with superior hybridization property, recognition orthogonality, and helical sense translational capability, significantly expands the scope of gamma PNA in biology, biotechnology, and molecular engineering.