The conditions that led to the formation of the first organisms and the ways that life originates from a lifeless chemical soup are poorly understood. The recent hypothesis of "RNA-peptide coevolution" suggests that the current close relationship between amino acids and nucleobases may well have extended to the origin of life. We now show how the interplay between these compound classes can give rise to new self-replicating molecules using a dynamic combinatorial approach. We report two strategies for the fabrication of chimeric amino acid/nucleobase self-replicating macrocycles capable of exponential growth. The first one relies on mixing nucleobase- and peptide-based building blocks, where the ligation of these two gives rise to highly specific chimeric ring structures. The second one starts from peptide nucleic acid (PNA) building blocks in which nucleobases are already linked to amino acids from the start. While previously reported nucleic acid-based self-replicating systems rely on presynthesis of (short) oligonucleotide sequences, self-replication in the present systems start from units containing only a single nucleobase. Self-replication is accompanied by self-assembly, spontaneously giving rise to an ordered one-dimensional arrangement of nucleobase nanostructures.