Inclusion Criteria:

• Histologically confirmed diagnosis of CD19-positive CLL with evidence of relapse/refractory disease.
• At least 28 days since the last chemotherapy or radiation prior to the first dosing of MDX-1342 and have recovered from any toxicity associated with such treatment or returned baseline.
• At least 28 days prior to the first dose of MDX-1342 since any major surgery.
• At least 18 years of age.
• At least 12 weeks life expectancy.
• ECOG Performance Status 0 to 2.
• Screening laboratory values must be met.
• Women must meet 1 of the following criteria: post-menopausal for at least 2 years; surgically incapable of bearing children or utilizing a reliable form of contraception.
• Med on corticosteroids must be tapered off the medication 14 days prior to the first dose of MDX-1342 and must remain off all corticosteroids during the Initial Treatment Phase and all Re-treatment Phases (except as indicated for Grade 3 infusion reactions). Corticosteroid use will be allowed during all Follow-up Phases.

Exclusion Criteria:

• Previous treatment with any other anti-CD19 antibody.
• Any other active malignancy within 2 years prior to enrollment excluding basal or squamous cell carcinoma of the skin or cervical carcinoma in situ.
• Any active, uncontrolled infection.
• Prior allogeneic bone marrow transplant.
• Active autoimmune disease requiring immunosuppressive therapy.
• Known current drug or alcohol abuse.
• Apparent active or latent tuberculosis (TB) infection (purified protein derivative (PPD) test is not required) as indicated by any of the following: PPD recently converted to positive, chest x-ray with evidence of infection, recent changes in fever/chill patterns.
• Patients who are pregnant or nursing.
• Any underlying medical condition which, in the Principal Investigator's opinion, will make the administration of MDX-1342 hazardous or obscure the interpretation of adverse events.
• Patients on concomitant chemotherapy, corticosteroids, investigational agents, growth factors cytokines, radiation therapy, or growth factors (GM-CSF or G-CSF may be used to treat neutropenia, however prophylactic use is prohibited). Hormonal therapy and biologic therapy for the treatment of CLL or other cancers is also prohibited.