In the nearly quarter-century since the first report of the Soai reaction, no other system has been documented to exhibit the remarkable features of self-replication with chiral amplification that characterize the Soai reaction. Because the chemistry involved in this reaction has little prebiotic relevance, the search continues for a prebiotically plausible autocatalytic reaction that amplifies enantiomeric excess. The features that such a reaction must exhibit include high selectivity, an inhibition mechanism for production of the minor enantiomer, high efficiency, and persistent self-replication under plausible concentration conditions. The discovery of a reaction or a reaction network embodying these features remains an elusive challenge.