Inclusion Criteria:

- >= 18 yrs of age, have B-cell CLL, failed at least 1 prior fludarabine-containing
regimen.

- Refractory to 1 fludarabine-containing regimen is defined as failure to achieve at
least PR to the last fludarabine-containing regimen received, or disease progression
while receiving the last fludarabine-containing regimen, or disease progression in
responders (i.e., achieved a PR or CR) within 6 mos of the last cycle of the last
fludarabine-containing regimen received (e.g., fludarabine monotherapy, FR, or FC) or
in responders (i.e., achieved a PR or CR ) within 24 mos of the last cycle of FCR.

- Intolerant to fludarabine is defined as discontinuation of therapy within 2 cycles
due to side effects/toxicity from the last fludarabine-containing regimen.

- ECOG score of <=1.

- Adequate coagulation, renal, & hepatic function at Screening as follows:

- Serum creatinine <= 2.0 mg/dL or calculated creatinine clearance >= 50 mL/min;

- AST & ALT <= 3.0 x ULN;

- Bilirubin <= 1.5 x ULN.

- Gilbert's Syndrome may have a Bilirubin > 1.5 x ULN; aPTT, PT, not to exceed 1.2 x
ULN.

- Adequate bone marrow (BM) independent of any growth factor support (with the
exception of subjects with BM heavily infiltrated with underlying disease [80% or
more] who may use growth factor support to achieve adequate BM) at Screening as
follows:

- ANC >= 1000/µL;

- Platelets >= 75,000/mm3 (entry platelet count must be independent of transfusion
within 14 days of Screening);

- Hemoglobin >= 9.0 g/dL.

- History of autologous BM transplant must be > 6 mos post transplant (prior to the 1st
dose of study drug) & have adequate BM independent of any growth factor support (with
the exception of subjects with BM that is heavily infiltrated with underlying disease
[80% or more] who may use growth factor support to achieve adequate BM) at Screening
as follows:

- ANC >= 1500/µL;

- Platelets >= 125,000/mm3;

- Hemoglobin >= 10.0 g/dL.

- Female subjects must be surgically sterile, postmenopausal (at least 1 year), or have
negative results on a pregnancy test.

- All female subjects not surgically sterile or postmenopausal (at least 1 year) &
non-vasectomized male subjects must practice birth control.

Exclusion Criteria:

- History/clinically suspicious for cancer-related CNS disease.

- Undergone allogeneic stem cell transplant.

- Undergone autologous stem cell transplant w/i 6 mos prior to 1st dose.

- History/predisposing condition of bleeding or currently exhibits signs of bleeding.

- Recent history of non-chemotherapy induced thrombocytopenic associated bleeding w/i 6
mos prior to 1st dose.

- Active peptic ulcer disease or other hemorrhagic esophagitis/gastritis.

- Active immune thrombocytopenic purpura or history of being refractory to platelet
transfusions w/i 1 yr prior to 1st dose.

- Currently receiving/requires anticoagulation therapy or any drugs or herbal
supplements that affect platelet function, with the exception of low-dose
anticoagulation medications used to maintain the patency of a central IV catheter.

- Significant history of cardiovascular disease, renal, neurologic, psychiatric,
endocrinologic, metabolic, immunologic, or hepatic disease.

- Positive for HIV, Hepatitis B, or Hepatitis C.

- Previous or current malignancies w/i the last 3 yrs:

- except adequately treated in situ carcinoma of the cervix uteri;

- basal or squamous cell carcinoma;

- in situ carcinoma of the bladder;

- or previous malignancy confined and surgically resected with curative intent.

- Has Prolymphocytic leukemia or Richter's transformation to an aggressive B-cell
malignancy.

- Exhibits evidence of other clinically significant uncontrolled condition(s)
including, but not limited to uncontrolled systemic infection or diagnosis of fever
and neutropenia w/i 1 week prior to study drug.

- Prior exposure to ABT-263.

- Received antibody therapy w/i 30 days prior to 1st dose.

- Received any anti-cancer therapy including chemotherapy, immunotherapy, radiotherapy,
hormonal, or any investigational therapy w/i 14 days prior to the 1st dose, or has
not recovered to therapy.

- Received steroid therapy for anti-neoplastic intent, w/i 7 days prior to the 1st dose
with the exception of inhaled steroids for asthma, topical steroids, or
replacement/stress corticosteroids.

- Received aspirin w/i 7 days prior to the 1st dose.

- Consumed grapefruit or grapefruit products w/i 3 days prior to 1st dose.

- Females pregnant or breast-feeding.