Patients with a diagnosis of CLL/SLL who do not meet the eligibility criteria for receiving Rituximab and Fludarabine (are not intermediate- or high-risk CLL/SLL), can enroll on the protocol for the purpose of donating cellular products. Such patients will not receive rituximab and fludarabine chemotherapy. At a later date, if it is documented that the patient does meet the criteria, then the patient may receive Rituximab and Fludarabine (after discussion with the Principal Investigator).