Mucositis is a serious side effect of cancer therapy and Peripheral Blood Stem Cell Transplant (PBSCT) which requires appropriate and effective management. Mucositis is a condition in which there is inflammation and ulceration of the mouth, throat and gut caused by damage to the mucosal barrier induced by chemo- and radiotherapy. Symptoms include pain, nausea, abdominal cramping, and vomiting. This study will investigate whether ATL-104, when administered as a swallowable mouthwash, is safe and well tolerated in patients undergoing PBSCT and to investigate its potential to reduce the level of severity of mucositis associated with PBSCT.