Inclusion Criteria:

- Clinical and phenotypic verification of B cell CLL and measurable disease.

- Immunophenotyping of the leukemic cells must demonstrate a monoclonal B cell
population with immunophenotype consistent with CLL

- Relapsed or refractory disease, defined by failure to achieve a partial response
within 6 months of initiation of therapy, or a 50% increase of baseline disease
measurements after achieving a clinical response.

- Not amenable to approved therapies.

- Prior Therapy: Must have progressed after purine-analog or alkylator based therapy,
or be considered inappropriate for chemo-immunotherapy due to one of the following:

- Del 17p, which is associated with poor response to chemo-immunotherapy, or

- Age greater than 70, or

- Age greater than 65 with one of the following:

- Grade 3 neutropenia, anemia, or thrombocytopenia attributable to cumulative
myelotoxicity from prior administration of cytotoxic agents (as documented by
bone marrow biopsy obtained since last prior therapy), or

- Clinically apparent autoimmune cytopenia which may be exacerbated by fludarabine
therapy, or

- Estimated creatinine clearance (eCCr) <70 mL/min (as determined by the
Cockcroft-Gault method), or

- Eastern Cooperative Oncology Group (ECOG) performance status greater than 0.

- Has recovered from the toxic effects of prior therapy to their clinical baseline.

- Subjects must be aged 18 years or older.

- Women of childbearing potential must agree not to become pregnant for the duration of
the study.

- Subjects must have at least one of the following indications for treatment:

- Symptomatic or progressive splenomegaly;

- Symptomatic lymph nodes, nodal clusters, or progressive lymphadenopathy;

- Progressive anemia (hemoglobin 11 g/dL);

- Progressive thrombocytopenia (platelets 100 x 109/L);

- Weight loss > 10% body weight over the preceding 6 month period;

- Fatigue attributable to CLL;

- Fever or night sweats for > 2 weeks without evidence of infection;

- Progressive lymphocytosis with an increase of > 50% over a 2-month period or an
anticipated doubling time of less than 12 months.

- Subjects must have an ECOG performance status of 0-2.

- Adequate hematologic function

- Adequate renal function

- Adequate hepatic function

- Adequate coagulation tests

Exclusion Criteria:

- Pregnant or breast-feeding women will not be entered on this study due to risks of
fetal and teratogenic adverse events as seen in animal/human studies.

- Patients who are currently receiving another investigational agent are excluded.

- Patients who have had chemotherapy (e.g., purine analogues, alkylating agents),
immunotherapy, radiation therapy, or participation in any investigational drug
treatment within 4 weeks of initiation of UC-961 or at any time during the study.

- Patients who have had prior (within 8 weeks of initiation of UC-961) or concurrent
antibody therapy directed against CLL (i.e., Rituxan and Campath)

- Current infection requiring parenteral antibiotics.

- Active infection with HIV, hepatitis B virus (HBV), or hepatitis C virus (HCV).

- Concurrent malignancy or prior malignancy within the previous 3 years (other than
completely resected carcinoma in situ, prostate cancer, or localized non-melanoma
skin cancer).

- Known central nervous system (CNS) involvement by malignancy.

- Untreated autoimmunity such as autoimmune hemolytic anemia, or immune
thrombocytopenia.

- Uncompensated hypothyroidism (defined as thyroid-stimulating hormone (TSH) greater
than 2x upper limit of normal not treated with replacement hormone).

- Presence of more than 55% pro-lymphocytes in peripheral blood. Patients with
Richter's transformation are not excluded.

- Insufficient recovery from surgical-related trauma or wound healing.

- Impaired cardiac function.

Minimum Eligible Age: 18 Years

Maximum Eligible Age: 70 Years

Eligible Gender: Both