RNA strand exchange through phosphor-nucleotidyl transfer reactions is an intrinsic chemistry promoted by group I intron ribozymes. We show here that Tetrahymena and Azoarcus ribozymes can promote RNA oligonucleotide recombination in either two-pot or one-pot schemes. These ribozymes bind one oligonucleotide, cleave following a guide sequence, transfer the 3' portion of the oligo to their own 3' end, bind a second oligo, and catalyze another transfer reaction to generate recombinant oligos. Recombination is most effective with the Azoarcus ribozyme in a single reaction vessel in which over 75% of the second oligo can be rapidly converted to recombinant product. The Azoarcus ribozyme can also create a new functional RNA, a hammerhead ribozyme, which can be constructed via recombination and then immediately promote its own catalysis in a homogeneous milieu, mimicking events in a prebiotic soup.