Inclusion Criteria:

- Histologically or cytologically confirmed chronic lymphocytic leukemia (CLL) by
NCI-WG immunophenotype and blood criteria

- Documentation of current or prior peripheral blood (PB) or bone marrow (BM)
immunophenotype compatible with CLL

- Patients who currently do not have > 5,000/mm³ absolute lymphocytosis are
eligible if they have previously met PB lymphocytosis criteria and have a
current immunophenotype documenting monoclonal B lymphocytosis
morphologically and immunophenotypically compatible with CLL

- Intermediate-risk (Rai stage I or II) or high-risk (Rai stage III or IV)
disease, including any of the following:

- Rai stage I disease with lymphocytosis and enlarged nodes

- Rai stage II disease with lymphocytosis plus splenomegaly and/or hepatomegaly
(nodes positive or negative)

- Rai stage III disease with lymphocytosis plus anemia

- Rai stage IV disease with lymphocytosis and thrombocytopenia

- Must require treatment with active disease, experiencing disease related symptoms, or
having deterioration of blood counts, meeting ≥ 1 of the following criteria:

- Presence of ≥ 1 of the following disease-related symptoms:

- Weight loss > 10% within the past 6 months

- Extreme fatigue (i.e., ECOG performance status 2: cannot work or unable to
perform usual activities)

- Fever > 100.5°F for 2 weeks without evidence of infection

- Night sweats without evidence of infection

- Evidence of progressive marrow failure, as manifested by worsening of anemia
(hemoglobin < 10 g/dL), thrombocytopenia (platelet count < 100,000/mm³), and/or
neutropenia (neutrophil count < 2,000/mm³)

- Massive (i.e., > 6 cm below left costal margin) or progressive splenomegaly or
discomfort from splenomegaly

- Massive nodes or clusters (i.e., > 10 cm in longest diameter), progressive
adenopathy, or discomfort from lymphadenopathy

- Deterioration of blood counts and/or progressive lymphocytosis, with an
increase of ≥ 10% documented over a 2-month period OR an anticipated doubling
time < 6 months

- Relapsed disease

- Must receive at least 1, but no more than 3, prior chemotherapy regimens with
any cytotoxic agent or antibody therapy

- No fludarabine refractory disease

- Responded to prior fludarabine without relapse or disease progression
for at least 6 months

- Patients with a history of Coombs-positive hemolytic anemia are eligible provided
recovery from treatment of hemolysis and off steroids

- No stage 0 CLL

- No known CNS involvement

- Life expectancy > 6 months

- ECOG performance status 0-2 OR Karnofsky performance status 70-100%

- Absolute neutrophil count ≥ 1,000/mm³

- Platelets ≥ 30,000/mm³

- Bilirubin ≤ 2 mg/dL

- AST/ALT ≤ 2.5 times upper limit of normal (ULN)

- Creatinine ≤ 1.5 times ULN OR creatinine clearance ≥ 60 mL/min (for patients with
creatinine levels above normal)

- No currently active second malignancy

- Not pregnant or nursing

- Negative pregnancy test

- Fertile patient must use effective contraception prior to and during study
participation

- No uncontrolled hypertension, defined as blood pressure (BP) > 150/100 mm Hg on 2
different measurements at least 1 day apart with either systolic or diastolic number
meeting this definition

- Patients may later enter the study, if they have achieved stable BP (i.e., <
140/90 mm Hg) on a regimen of ≤ 2 drugs after 6-8 weeks of therapy

- No history of allergic reactions attributed to compounds of similar chemical or
biologic composition to sorafenib

- No uncontrolled intercurrent illness including, but not limited to, any of the
following:

- Symptomatic congestive heart failure

- Unstable angina pectoris

- Cardiac arrhythmia

- Psychiatric illness or social situations that would limit compliance with the
study requirements

- No active infection requiring systemic antibiotics

- No evidence of bleeding diathesis

- No evidence of bowel perforation or obstruction risk

- No swallowing dysfunction leading to difficulty taking the study drug

- See Disease Characteristics

- Recovered from prior therapy

- At least 2 weeks since prior antibiotic therapy

- At least 4 weeks since prior chemotherapy (6 weeks for nitrosoureas or mitomycin C)
or radiotherapy

- At least 12 weeks since prior monoclonal antibody

- Concurrent warfarin for anticoagulation allowed provided all of the following are
met:

- On a stable therapeutic dose

- INR ≤ 3

- No active bleeding or pathological condition that carries high-risk of bleeding

- No prior MAPK signaling inhibitor agents or anti-angiogenesis agents

- No concurrent combination anti-retroviral therapy for HIV-positive patients

- No concurrent cytochrome P450 enzyme-inducing antiepileptic drugs (phenytoin,
carbamazepine, or phenobarbital), rifampin, or Hypericum perforatum (St. John's wort)

- No other concurrent investigational agents