An RNA ligase ribozyme that catalyzes the joining of RNA molecules of the opposite chiral handedness was optimized for the ability to synthesize its own enantiomer from two component fragments. The mirror-image D- and L-ligases operate in concert to provide a system for cross-chiral replication, whereby they catalyze each other's synthesis and undergo mutual amplification at constant temperature, with apparent exponential growth and a doubling time of about 1 h. Neither the D- nor the L-RNA components alone can achieve autocatalytic self-replication. Cross-chiral exponential amplification can be continued indefinitely through a serial-transfer process that provides an ongoing supply of the component D- and L-substrates. Unlike the familiar paradigm of semiconservative nucleic acid replication that relies on Watson-Crick pairing between complementary strands, cross-chiral replication relies on tertiary interactions between structured nucleic acids "across the mirror." There are few examples, outside of biology, of autocatalytic self-replication systems that undergo exponential amplification and there are no prior examples, in either biological or chemical systems, of cross-chiral replication enabling exponential amplification.