The goal of this clinical research study is to learn if eltrombopag can help to increase the number of platelets in patients with CLL. The safety of this drug will also be studied.

The Study Drug:

When the number of platelets in your body gets too low, it can cause bleeding, which may cause serious health problems and/or prevent you from receiving chemotherapy. Eltrombopag is designed to act like a protein in your body that helps make platelets. This may help increase your platelet counts.

Study Drug Administration:

You will take pills of the study drug by mouth 1 time each day on an empty stomach (1 hour before or 2 hours after a meal). You should take the pills with 1 cup (8 ounces) of water. You should wait at least 4 hours between taking eltrombopag and eating foods with calcium (dairy products and/or juices with added calcium) or taking drugs/supplements with iron, calcium, aluminum, magnesium, selenium and/or zinc. Other drugs may also affect eltrombopag. Be sure to tell your doctor about any drugs and/or supplements you may be taking.

During your study visits, your doctor will check your platelet counts to see if they improve. If they do not improve, your dose of study drug may be increased. Your doctor will instruct you on each dose of eltrombopag you should take.

Do not take more than 1 dose of eltrombopag on any one day. If you forget to take a dose, you should skip the missed dose and continue your regular dosing schedule. Do not take a double dose to make up for a missed one.

Study Visits:

Each study "cycle" will be 28 days.

Each week during Cycle 1, then every 2 weeks during Cycles 2 and 3:

• You will have a physical exam, including measurement of your vital signs.
• You will be asked about any bleeding that may have occurred since the last study visit.
• Blood (about 1 tablespoon) will be drawn for routine tests.

On Day 1 (+/- 7 days) of Cycles 4 and beyond:

• You will have a physical exam.
• You will be asked about any bleeding that may have occurred since the last study visit.
• Blood (about 1 tablespoon) will be drawn for routine tests.
• You will also have a bone marrow aspirate/biopsy to check the status of the disease and to check your platelet counts. This test will only be performed every 3 cycles.

Length of Study Participation:

You may continue taking the study drug for as long as the doctor thinks it is in your best interest. You will no longer be able to take the study drug if you require other treatment for CLL or if intolerable side effects occur.

Follow-Up:

After you stop taking eltrombopag for any reason, your platelet counts may drop. This may increase your risk of bleeding. Blood (about 1 tablespoon) will be drawn each week for 4 weeks to check your platelet counts.

This is an investigational study. Eltrombopag is FDA approved and commercially available for use in chronic immune thrombocytopenic purpura (ITP - severe bleeding due to platelet destruction by the immune system). The use of this drug in patients with CLL is investigational.

Up to 36 patients will take part in this study. All will be enrolled at MD Anderson.

Inclusion Criteria:

1. Diagnosis of chronic lymphocytic leukemia (CLL) or small lymphocytic lymphoma (SLL)
2. Age >/= 18 years
3. PLT transfusion-dependent, defined as need for transfusion to maintain PLT count >/=20K/µL, or the average of two (non-transfused) PLT counts taken within 2 weeks of the screening period </=50K/µL, with no individual count >55K/µL
4. Patients with ITP must have failed at least 1 prior treatment for ITP including one of the following: corticosteroids, rituximab, splenectomy, cyclosporine
5. At least 3 weeks must have elapsed since the last chemotherapy treatment for CLL
6. ECOG performance status (PS) \

Up to 4 years