The goal of this clinical research study is to learn if dasatinib can help to control Chronic Lymphocytic Leukemia (CLL). The safety of the drug will also be studied.

Optional Procedures: You will be asked to have additional blood samples drawn. These samples will be used to see how the disease is responding to the drug.

Dasatinib is designed to interfere with a type of protein that appears to be important for the survival of CLL cells.

If you are found to be eligible to take part in this study, you will take dasatinib by mouth twice a day. You will be instructed to take dasatinib in the morning and in the evening.

You will have an electrocardiogram (ECG-a test of the electrical activity of your heart) and a physical exam once every 3 months while on study. Blood (about 2-3 teaspoons) will be drawn for routine tests once a week for 1 month and then once a month for the rest of your treatment on this study. A bone marrow biopsy and aspiration will be performed, as needed, to check the status of the disease. To collect a bone marrow aspirate and biopsy, an area of the hip or chest bone is numbed with anesthetic, and a small amount of bone marrow and bone is withdrawn through a large needle.

Dasatinib will be given for as long as you are responding. You will be taken off study if the disease gets worse or intolerable side effects occur.

This is an investigational study. Dasatinib is not FDA-approved for CLL, and it has been authorized for use in research only. Up to 25 patients will take part in this multicenter study. Up to 25 will be enrolled at M. D. Anderson.

Optional Procedures: If you agree, blood samples (about 2 tablespoons each time) will be collected before therapy starts, at 3-4 hours after the first dose, and at 3 months on therapy. These blood draws will be done when other routine tests are done. No additional needle sticks will be needed. The blood will be used to see how the disease is responding to the drug.

You do not have to agree to take part in the optional procedures in order to receive treatment on this study.

Inclusion Criteria:

1. Diagnosis of CLL, Small lymphocytic lymphoma (SLL), or -cell prolymphocytic leukemia (T-PLL).
2. Previously treated with chemotherapy or monoclonal antibodies.
3. All patients with Rai stage III-IV are eligible. - OR - Patients with Rai stage 0-II who meet one or more indication for treatment as defined by the NCI-sponsored Working Group are eligible:Massive or progressive splenomegaly; Massive lymph nodes, nodal clusters, or progressive lymphadenopathy; Grade 2 or 3 fatigue, fever >/= 100.5 degrees F, night sweats for > 2 weeks w/o documented infection, presence of weight loss >/= 10% over the preceding 6 months; Progressive lymphocytosis with increase in lymphocyte count of >/= 50% over a 2-month period or an anticipated doubling time of < 6 months.
4. Serum bilirubin less than 2mg/dL, serum creatinine less than 2mg/dL unless abnormality is considered due to CLL by investigator.
5. The Eastern Cooperative Oncology Group (ECOG) Performance Status < 3.
6. Patients must sign an informed consent indicating they are aware of the investigational nature of this study, in keeping with the policies of the hospital.
7. Sexually active women of childbearing potential must use birth control during study in manner that risk of failure is minimized. Prior to study enrollment women of childbearing potential must be advised of importance of avoiding pregnancy during trial and potential risk factors for unintentional pregnancy. MUST have negative pregnancy test. If pregnancy test is positive patient must not receive investigational product and must not be enrolled in study. Men enrolled on study should understand risks to sexual partner of childbearing potential and practice effective birth control.
8. Inclusion of women and minorities: As per NIH policy, women and members of minorities will be included in this protocol as they are referred in the relevant populations. There are no exclusions of women or minorities based on the study objectives.
9. New York Heart Association (NYHA) Class < 3
10. Patients must sign informed consent.

Exclusion Criteria:

1. Pregnant or breast-feeding women are excluded.
2. Patients may not receive concurrent chemotherapy, radiotherapy, or immunotherapy. Localized radiotherapy to an area not compromising bone marrow function does not apply, nor do hematopoietic growth factors such as erythropoietin, G-CSF, GM-CSF etc.
3. Patients must not have untreated or uncontrolled life-threatening infection.
4. Uncontrolled angina within 3 months; diagnosed or suspected congenital long QT syndrome; any history of clinically significant ventricular arrhythmias; prolonged QTc interval (> 450 msec); uncontrolled hypertension; significant bleeding disorder unrelated to cancer; patients currently taking drugs that are generally accepted to have a risk of causing Torsades de Pointes.
5. Medications that inhibit platelet function (i.e., aspirin, dipyridamole, epoprostenol, eptifibatide, clopidogrel, cilostazol, abciximab, ticlopidine, and any non-steroidal anti-inflammatory drug) or Anticoagulants (warfarin, heparin/low molecular weight heparin [e.g., danaparoid, dalteparin, tinzaparin, enoxaparin]).

6 Years, 3 Months