Sorafenib for the Treatment of Chronic Lymphocytic Leukemia (CLL)

Inclusion Criteria: * Diagnosis of relapsed or refractory CLL. * Experiencing progressive disease with an iwCLL-WG indication to receive therapy. * Age ≥ 18 years. * ECOG performance status ≤ 2 at study entry. * Adequate organ and marrow function as defined below: * platelets ≥ 50 x 109/L * serum creatinine ≤ 1.5 mg/dL * total bilirubin ≤ 1.5 mg/dL * AST(SGOT)/ALT(SPGT) ≤ 2 X institutional upper limit of normal or if known liver involvement \<5X institutional upper limit of normal * Women of child-bearing potential and men must agree to use adequate contraception (hormonal or barrier method of birth control; abstinence) prior to study entry, for the duration of study participation, and for 90 days following completion of therapy. Should a woman become pregnant or suspect she is pregnant while participating in this study, she should inform her treating physician immediately. * Ability to understand and the willingness to sign a written informed consent. Exclusion Criteria: * No investigational agents within 28 days prior to entering the study. * No concurrent use of other anti-cancer agents or treatments. * No congestive heart failure \> class II NYHA. Patients must not have unstable angina (anginal symptoms at rest) or new onset angina (beginning within the last 3 months) or myocardial infarction within the past 6 months. * No known brain metastases (progressive neurologic dysfunction may confound the evaluation of neurologic and other adverse events). * No cardiac ventricular arrhythmias requiring anti-arrhythmic therapy. * No uncontrolled hypertension defined as systolic blood pressure \> 140 mmHg or diastolic pressure \> 90 mmHg, despite optimal medical management. * No known active Hepatitis or HIV. * No history of allergic reactions attributed to compounds sorafenib or its excipients. * No uncontrolled intercurrent illness such as ongoing or active infection (fungal, bacterial, and/or viral), CTCAE grade 2 or greater. * No thrombolic or embolic events such as a cerebrovascular accident including transient ischemic attacks within the past 6 months. * No serious non-healing wound, ulcer, or bone fracture. * No major surgery, open biopsy or significant traumatic injury within 4 weeks of first study drug. * No condition that may impair the patient's ability to swallow whole pills. * Patient must not have any malabsorption problem. * Patients receiving St. John's Wort or rifampin (rifampicin) are ineligible. * Patients with uncontrolled Autoimmune Hemolytic Anemia (AIHA) or autoimmune thrombocytopenia (ITP) are ineligible. * Patients must not be experiencing psychiatric illness/social situations that would limit compliance with study requirements. * Patients must not be pregnant or nursing due to the potential for congenital abnormalities and the potential of this regimen to harm nursing infants. * Subjects with any previously untreated or concurrent cancer that is distinct in primary site or histology from CLL except cervical cancer in-situ, treated basal cell carcinoma, squamous cell carcinoma of the skin, or superficial bladder tumor (Ta and Tis). Subjects surviving a cancer that was curatively treated and without evidence of disease for more than 3 years before study entry are allowed. All cancer treatments must be completed at least 3 years prior to study entry (ie, signature date of the informed consent form).