The non-enzymatic replication of RNA is thought to have been a critical process required for the origin of life. One unsolved difficulty with non-enzymatic RNA replication is that template-directed copying of RNA results in a double-stranded product. After strand separation, rapid strand reannealing outcompetes slow non-enzymatic template copying, which renders multiple rounds of RNA replication impossible. Here we show that oligoarginine peptides slow the 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, all 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 to enable further rounds of replication suggests one mechanism by which short non-coded peptides could have enhanced early cellular fitness, and potentially explains how longer coded peptides, that is, proteins, came to prominence in modern biology.