This trial is testing if hyperbaric oxygen therapy is safe and effective for patients with certain types of chronic leukemia undergoing stem cell transplantation. The therapy involves breathing pure oxygen in a pressurized chamber to help the body heal and fight infections. Researchers hope it will improve outcomes like the success of the transplant and reduce problems like inflammation and infections. Hyperbaric oxygen therapy has been studied for its potential to improve outcomes in patients undergoing stem cell transplantation by enhancing the success of the transplant and reducing problems.