The first ribozymes are thought to have emerged at a time when RNA replication proceeded via nonenzymatic template copying processes. However, functional RNAs have stable folded structures, and such structures are much more difficult to copy than short unstructured RNAs. How can these conflicting requirements be reconciled? Also, how can the inhibition of ribozyme function by complementary template strands be avoided or minimized? Here, we show that short RNA duplexes with single-stranded overhangs can be converted into RNA stem loops by nonenzymatic cross-strand ligation. We then show that loop-closing ligation reactions enable the assembly of full-length functional ribozymes without any external template. Thus, one can envisage a potential pathway whereby structurally complex functional RNAs could have formed at an early stage of evolution when protocell genomes might have consisted only of collections of short replicating oligonucleotides.