Inclusion Criteria:

- Adult men or women at least 18 years of age;

- Written informed consent and Heath Insurance Portability and Accountability Act
(HIPAA) authorization (applies to covered entities in the USA only) obtained from the
patient prior to performing any study-related procedures, including screening visits;

- Previous confirmation of B-cell CLL with a characteristic immunophenotype by flow
cytometry;

- MRD positivity, determined by 4-color flow cytometry of bone marrow or peripheral
blood in all patients following previous therapy for CLL;

- Measurable and/or residual disease following previous therapy for CLL as follows:

1. Measurable disease, as determined by NCI-WG criteria, following standard
first-line or salvage therapy; this includes patients with PD, SD, or PR (Phase
1 only);

2. Residual disease as determined by measurable disease (ie, PD, SD, or PR) or by
MRD positivity, determined by 4-color flow cytometry of bone marrow and/or
peripheral blood in patients with CR or nPR (Phase 2 only);

- Time from completing last therapy for CLL is ≥ 3 months but ≤ 1 year;

- Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2;

- Presence of live-in companion (relative or friend) who agrees to NOT leave the
patient unattended for > 8 hours per day;

- Patient agrees to refrain from engaging in hazardous occupations or activities
requiring complete mental alertness such as operating machinery or driving a motor
vehicle;

- Females, unless surgically sterile or at least 1 year post-menopausal, must use an
effective method of avoiding pregnancy (including oral, transdermal, or implanted
contraceptives, intrauterine device, female condom with spermicide, diaphragm with
spermicide, cervical cap, abstinence, use of a condom with spermicide by the sexual
partner or sterile sexual partner) for 21 days prior to the first dose of MEDI-538,
and must agree to continue using such precautions through 3 months after the last
dose of MEDI-538. Cessation of birth control after this point should be discussed
with a responsible physician. Males, unless surgically sterile, must likewise use an
effective method of birth control (condom with spermicide) and must agree to continue
using such precautions through 3 months after the last dose of MEDI-538;

- Hemoglobin ≥ 10.0 g/dL and platelets > 75.0 x 109/L;

- Total bilirubin ≤ 1.5 x ULN; aspartate transaminase (AST), alanine transaminase
(ALT), amylase and lipase ≤ 2 x ULN;

- Serum creatinine ≤ 2 x ULN and creatinine clearance ≥ 50 mL/min;

- Absolute neutrophil count (ANC) > 1.0 × 109/L; and

- For patients who have received previous treatment with alemtuzumab, CD4 counts must
be > 200 cells/μL with a negative status for cytomegalovirus (CMV) antigen.

Exclusion Criteria:

- Receipt of MEDI-538 in any previous clinical study;

- History of allergy or reaction to any component of the MEDI-538 formulation;

- History of malignancy other than CLL within 5 years prior to study entry, with the
exception of basal cell carcinoma of the skin or carcinoma in situ of the cervix
successfully treated with curative therapy;

- Fludarabine-refractory CLL, defined as failure to achieve a PR or CR/nPR to at least
one fludarabine-containing regimen, disease progression while on fludarabine
treatment, or disease progression in responders within 6 months of last dose of
fludarabine;

- Known or suspected CNS involvement;

- Clinical history of significant CNS pathology, eg, uncontrolled headaches, multiple
occurrences of confusion, dementia, multiple previous infarcts, or major brain
surgery;

- Active infection or known bacteremia. Patients with documented evidence of culture
positive sepsis or active infection requiring IV antibiotic therapy must complete a
full course of antibiotic treatment with no clinical or laboratory evidence of
bacterial infection at least 2 weeks prior to starting therapy with MEDI-538.

- Vaccination (either preventive or therapeutic for infectious disease or cancer)
within 2 weeks prior to initiation of MEDI-538;

- Infection with human immunodeficiency virus (HIV-1 or HIV-2), chronic infection with
hepatitis B or C, or acute infection with hepatitis A;

- History of serious, chronic autoimmune disease, eg, rheumatoid arthritis, systemic
lupus erythematosus, and multiple sclerosis;

- Elective surgery planned during the study period through 30 days after
discontinuation of MEDI-538;

- Autologous stem cell transplantation within 26 weeks prior to study entry;

- Allogenic stem cell transplantation or any other solid organ transplant;

- Regular dose of systemic corticosteroids during the 4 weeks prior to initiation of
MEDI-538 or anticipated need of corticosteroids exceeding prednisone 20 mg/day or
equivalent during the trial, or any other systemic immunosuppressive therapy within 4
weeks prior to study entry;

- Any contraindication to chronic anticoagulation with low-molecular weight heparin
(LMWH);

- Inability for safe placement and prolonged use (at least 4 weeks) of a central venous
catheter;

- Contraindication to any of the protocol-specified concomitant medications
(methylprednisolone, antacids, or antihistamines) during this study;

- Presence of known human anti-murine antibodies or hypersensitivity to
immunoglobulins;

- Pregnancy (females of childbearing potential must have a negative urine pregnancy
test on the day of the first dose of MEDI-538, prior to dosing) or nursing;

- Evidence of any uncontrolled systemic disease (other than CLL), including autoimmune
hemolytic anemia;

- Any finding upon physical examination or history of any disease or behavior that, in
the opinion of the investigator or medical monitor, may compromise the safety of the
patient in the study or confound the analysis of the study; or

- Inability to meet social environment requirements for outpatient therapy (see Section
3.3.4.2).