E1912

Approximately 519 people will take part in this research study.   Fludarabine and cyclophosphamide have been approved by the FDA for the treatment of chronic lymphocytic leukemia (CLL). Rituximab is approved for the treatment of CLL when given in combination with fludarabine and cyclophosphamide. Ibrutinib was previously studied in patients with CLL, and has been approved by the FDA for use in previously treated CLL patients. In this study, ibrutinib is investigational because it will be given to previously untreated CLL patients and administered in combination with rituximab. Before entering the study, patients will need to have a physical examination, blood tests, pregnancy test (for women of childbearing potential), and a bone marrow aspirate and biopsy to determine if they can be in the study. Those who qualify and choose to take part will have blood tests, CT scans of the chest, abdomen and pelvis, bone marrow aspirate and biopsy, and a quality of life survey before, during and after therapy. Patients who choose to take part will be randomly assigned to one of two arms. Those assigned to Arm A will receive ibrutinib and rituximab. Ibrutinib will be given by mouth daily for 28 days out of every 28 days. Each 28-day period is called a cycle. Participants on Arm A will also be given allopurinol for at least the first 14 days of treatment during Cycle 1 and Cycle 2 to protect their kidneys from the dying leukemia cells. The ibrutinib capsules should be taken at the same time every day with a glass of water, at least 30 minutes before eating or at least 2 hours after a meal. The ibrutinib capsules must not be dissolved. Starting during the second cycle, rituximab will be given by intravenous (IV) infusion (through a needle in a vein in the arm) over 4 hours of days 1 and 2 of cycle 2 and then on day 1 of cycles 3-7. There will be a total of 6 doses of rituximab. After cycle 7, no rituximab will be given, but the participant will continue to receive ibrutinib by mouth once daily as long as there is evidence that it is helping and the participant is tolerating the medication. Those assigned to Arm B will receive rituximab, fludarabine and cyclophosphamide. Each 28-day period is called a cycle. As long as the participant is tolerating treatment and there is evidence it is helping their CLL, they will receive 6 cycles of treatment. During the first cycle, rituximab will be given by intravenous infusion (IV) over 4 hours on days 1 and 2. During cycles 2-6, rituximab will be given on day 1 of every 28 days. There will be a total of 7 doses of rituximab. Fludarabine will also be given by IV infusion over a period of 30 minutes on the first 3 days of each cycle. Cyclophosphamide will also be given by IV infusion over 30 minutes each day on the first 3 days of each cycle. Participants on Arm B will also receive a pill called allopurinol for at least the first 14 days of treatment to protect their kidneys from the dying leukemia cells. After participants on Arm B finish 6 cycles of treatment, they will enter observation. Participants will be seen by their treating doctor every 3 months. Participants will be required to complete a pill calendar if they are assigned to the arm that receives ibrutinib.