A Study of Different Doses of Ibrutinib in Participants With Chronic Lymphocytic Leukemia (CLL)

Study Drug Administration: Each study cycle is 28 days. If you are found to be eligible to take part in this study, you will take ibrutinib capsules by mouth every day for 3 cycles. Each dose of ibrutinib should be taken at about the same time, either with or without food. During Cycle 1, you will receive the highest dose of ibrutinib (the dose that is currently FDA approved). You will take 3 capsules each day during Cycle 1. During Cycle 2, you will receive the second-highest dose and you will take 2 capsules each day. During Cycle 3, you will take the lowest dose of ibrutinib and you will take 1 capsule each day. You must swallow the ibrutinib capsules whole without opening, breaking, or chewing them. You will be given a study drug diary to keep track of each dose of ibrutinib taken, including the time the dose was taken, any missed or vomited doses and the reason for missing the dose, and any doses that you vomited. Study Visits: On Days 1, 8 and 28 of each cycle blood (about 1-2 tablespoons total) will be drawn before your dose of ibrutinib and then at 4 and 24 hours after your dose for pharmacodynamic (PD) and pharmacokinetic (PK) testing, to help researchers understand how ibrutinib works in the body, and to learn if the dose you are taking is as effective as other doses (Exception: there will be no 4-hour blood draw on day 28). PK testing measures the amount of study drug in the body at different time points. PD testing measures how the level of study drug in your body may affect the disease. You will need to return to the clinic on the following day (Days 2, 9 and 29 of each cycle \[Day 1 of the next cycle\]) for the last blood draw. On Day 28 of each cycle: * You will have a physical exam * Blood (about 1-2 tablespoons) will be drawn for routine tests. * You will have an EKG. Length of Study: You may receive ibrutinib on this study for up to 3 cycles. After this time, you will continue treatment for CLL as directed by your doctor. This may or may not include ibrutinib. If you do continue to take ibrutinib after the study is over, your doctor will determine the best dose for you to be taking. You will no longer be able to take the study drug if the disease gets worse, if intolerable side effects occur, or if you are unable to follow study directions. Your participation in this study will be over after your last dose of ibrutinib (after the end of Cycle 3). This is an investigational study. Ibrutinib is FDA approved and commercially available for the treatment of CLL. It is considered investigational to compare 3 different doses of ibrutinib. The study doctor can explain how the study drug is designed to work. Up to 12 participants will be enrolled in this study. All will take part at MD Anderson.