The replication of nucleic acids is a prerequisite for the survival and evolution of living systems. Before the advent of protein synthesis, genetic information was most likely stored on and replicated by RNA. However, experimental systems for sustained RNA-dependent RNA-replication are difficult to realise due to the high thermodynamic stability of duplex products and the low chemical stability of catalytic polynucleotides. Using a derivative of a group I intron as a model for an RNA replicase, we show that heated air-water interfaces exposed to a plausible CO2-rich atmosphere drive complete cycles of plus and minus strand replication. The reaction is driven by autonomous oscillations in salt concentrations and pH that transiently destabilise RNA duplexes. Newly synthesised strands can dissociate from their templates and adopt catalytically active conformations. Our results suggest that an abundant Hadean microenvironment may have promoted the replication of RNAs while maintaining the activity of the synthesised ribozymes.