Noncontiguous recombination (NCR) is a method to identify pieces of structure that can be swapped among homologous proteins to create new, chimeric proteins. These “blocks” are encoded by elements of sequence that are not necessarily contiguous along the polypeptide chain. We used NCR to design a library in which blocks of structure from Hypocrea jecorina cellobiohydrolase I (Cel7A) and its two thermostable homologues from Talaromyces emersonii and Chaetomium thermophilum are shuffled to create 531,438 possible chimeric enzymes. We constructed a maximally informative subset of 35 chimeras to analyze this library and found that the blocks contribute additively to the stability of a chimera. Within two highly stabilizing blocks, we uncovered six single amino acid substitutions that each improve the stability of H. jecorina cellobiohydrolase I by 1–3 °C. The small number of measurements required to find these mutations demonstrates that noncontiguous recombination is an efficient strategy for identifying stabilizing mutations.