Molecular replication, a fundamental process of life, has in recent years been the subject of laboratory investigations using simple chemical systems. Whereas the work of Rebek's group has focused on molecular architectures not known in living systems, self-replicating and template-based self-assembling systems based on nucleotides are regarded as potential models for exploring the evolution of replicating systems on the early Earth. Previous replicating oligonucleotides have been of the single-stranded, self-complementary type: small oligonucleotide fragments are assembled on a pre-existing template and linked to form an exact copy of the template. This process cannot easily be reiterated, however, because of the strong binding of the newly formed strand to the original template. Furthermore, DNA replication in living systems operates by complementarity rather than self-complementarity--each newly assembled strand is complementary to, rather than identical to, its template--and the replication process starts and finishes with double helices. Here we report the self-replication of palindromic (symmetrical) duplex DNA-like oligonucleotides, 24 monomers long, in the absence of enzymes by means of a cycle that transfers information from template to copy and is potentially capable of extension to include non-symmetrical sequences, selection and mutation. Replication proceeds by a chemical process involving the formation of an intermediate triplex structure, and is sequence-selective in the sense that mismatches impair its efficiency. These results indicate that DNA-like double-helical molecules can replicate without assistance from proteins, a finding that may be relevant both to the appearance of replicating systems on the early Earth and to the development of new approaches to DNA amplification.