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).