The nonenzymatic replication of RNA is thought to have been a critical aspect of the chemistry of the origin of life. One unsolved difficulty with nonenzymatic RNA replication is that template-directed copying of RNA results in a double-stranded product; following strand separation, rapid strand reannealing outcompetes slow nonenzymatic template copying, rendering multiple rounds of RNA replication impossible. Here we show that oligoarginine peptides slow annealing of complementary oligoribonucleotides by up to several thousand-fold; however, short primers and activated monomers can still bind to template strands, and template-directed primer extension can still occur within a phase-separated condensed state, or coacervate. Furthermore, we show that within this phase, partial template copying occurs even in the presence of full-length complementary strands. This method for enabling further rounds of replication suggests one mechanism by which short, non-coded peptides could have enhanced early cellular fitness, potentially explaining how longer, coded peptides, i.e. proteins, came to prominence in modern biology.