Inclusion Criteria: - Life expectancy of at least 12 weeks - Histological documentation of epithelial ovarian cancer (EOC), primary peritoneal cancer (PPC), or fallopian tube cancer (FTC) - Availability of an adequate tumor specimen verified prior to enrollment - Advanced, epithelial ovarian, primary peritoneal, or fallopian tube cancer that has progressed or relapsed during or within 6 months of the most recent treatment with a platinum-containing chemotherapy regimen, and for which no standard therapy exists - For patients in the dose-expansion cohort of the study only, not more than two prior chemotherapy regimens for the treatment of platinum-resistant ovarian cancer - Measurable disease with at least one lesion that can be accurately measured in at least one dimension - Documented willingness to use an effective means of contraception for women of childbearing potential Exclusion Criteria: - Anti-tumor therapy, including chemotherapy, biologic, experimental, or hormonal therapy within 4 weeks prior to Day 1 - Palliative radiation to bone metastases within 2 weeks prior to Day 1 - Major surgical procedure within 4 weeks prior to Day 1 - Known active bacterial, viral, fungal, mycobacterial, or other infection (including HIV and atypical mycobacterial disease, but excluding fungal infections of the nail beds) - Current Grade >1 toxicity (except alopecia and anorexia) from prior therapy or Grade >1 neuropathy from any cause - History of severe allergic or anaphylactic reactions to monoclonal antibody therapy (or recombinant antibody-related fusion proteins) - Clinically significant history of liver disease, including viral or other hepatitis, current alcohol abuse, or cirrhosis - Untreated or active central nervous system (CNS) metastases (progressing or requiring anticonvulsants or corticosteroids for symptomatic control). Patients with a history of treated CNS metastases are eligible, provided that they meet all of the following criteria: evaluable or measurable disease outside the CNS Radiographic demonstration of improvement upon the completion of CNS-directed therapy and no evidence of interim progression between the completion of CNS-directed therapy and the screening radiographic study, and the screening CNS radiographic study is ≥ 8 weeks since completion of radiotherapy and ≥ 4 weeks since the discontinuation of corticosteroids and anticonvulsants. - Any other diseases, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates the use of an investigational drug or that may affect the interpretation of the results or render the patient at high risk from treatment complications - Evidence of significant uncontrolled concomitant diseases, such as cardiovascular disease (including stroke, New York Heart Association Class III or IV cardiac disease or myocardial infarction within 6 months prior to screening, unstable arrhythmias, and unstable angina); nervous system, pulmonary (including obstructive pulmonary disease and history of symptomatic bronchospasm), renal, hepatic, endocrine, or gastrointestinal disorders; or a serious non-healing wound or fracture - Pregnancy or breast-feeding