We introduce a method of in vitro recombination or "DNA shuffling" to generate libraries of evolved enzymes. The approach relies on the ordering, trimming, and joining of randomly cleaved parental DNA fragments annealed to a transient polynucleotide scaffold. We generated chimeric libraries averaging 14.0 crossovers per gene, a several-fold higher level of recombination than observed for other methods. We also observed an unprecedented four crossovers per gene in regions of 10 or fewer bases of sequence identity. These properties allow generation of chimeras unavailable by other methods. We detected no unshuffled parental clones or duplicated "sibling" chimeras, and relatively few inactive clones. We demonstrated the method by molecular breeding of a monooxygenase for increased rate and extent of biodesulfurization on complex substrates, as well as for 20-fold faster conversion of a nonnatural substrate. This method represents a conceptually distinct and improved alternative to sexual PCR for gene family shuffling.