The purpose of this study is to determine if treatment with paclitaxel plus AMG 386 is superior to paclitaxel plus placebo in women with recurrent partially platinum sensitive or resistant epithelial ovarian cancer, primary peritoneal cancer or fallopian tube cancer.

AMG 386 is a man-made medication that is designed to stop the development of blood vessels in cancer tissues. Cancer tissues rely on the development of new blood vessels, a process called angiogenesis, to obtain a supply of oxygen and nutrients to grow.

Inclusion Criteria:

• Female 18 years of age or older at the time the written informed consent is obtained
• Gynecologic Oncology Group (GOG) Performance Status of 0 or 1
• Life expectancy >= 3 months (per investigator opinion)
• Histologically or cytologically documented invasive epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer (Subjects with pseudomyxoma , mesothelioma, unknown primary tumor, sarcoma, or neuroendocrine histology, with borderline ovarian cancer, ie, subjects with low malignant potential tumors, and with clear cell or mucinous histology are excluded)
• Subjects must have undergone surgery for ovarian cancer, primary peritoneal cancer, or fallopian tube cancer including at least a unilateral oophorectomy
• Radiologically evaluable disease per Response Evaluation Criteria in Solid Tumors (RECIST) 1.1 with modifications
• Subjects must have had one prior platinum-based chemotherapeutic regimen for management of primary disease containing carboplatin, cisplatin, or another organoplatinum compound. This initial treatment may have included intraperitoneal therapy, high-dose therapy, consolidation therapy, bevacizumab or extended therapy administered after surgical or non-surgical assessment.
• Adequate organ and hematological function
• Generally well controlled blood pressure with systolic blood pressure <= 140 mmHg and diastolic blood pressure <= 90 mmHg prior to randomization. The use of anti-hypertensive medications to control hypertension is permitted
• Radiographically documented disease progression either on or following the last dose of prior chemotherapy regimen for epithelial ovarian cancer, primary peritoneal cancer, or fallopian tube cancer

Exclusion Criteria:

• Subjects who have received more than 3 previous regimens of anti-cancer therapy for epithelial ovarian, primary peritoneal or fallopian tube cancers
• Subjects who have received paclitaxel as consolidation therapy, maintenance, or monotherapy are excluded
• Subjects with primary platinum-refractory disease
• Subjects with platinum-free interval (PFI) > 12 months from their last platinum based therapy
• Radiotherapy <= 14 days prior to randomization. Subjects must have recovered from all radiotherapy-related toxicities
• Previous abdominal or pelvic radiotherapy
• History of arterial or venous thromboembolism within 12 months prior to randomization
• History of clinically significant bleeding within 6 months prior to randomization
• History of central nervous system metastasis
• Has not yet completed a 21 day washout period prior to randomization for any previous anti cancer systemic therapies (30 days for prior bevacizumab)
• Enrolled in or has not yet completed at least 30 days (prior to randomization) since ending other investigational device or drug, or currently receiving other investigational treatments
• Unresolved toxicities from prior systemic therapy that are Common Terminology Criteria for Adverse Events (CTCAE) Version 3.0 >= Grade 2 in severity except alopecia
• Known active or ongoing infection (except uncomplicated urinary tract infection [UTI]) within 14 days prior to randomization
• Currently or previously treated with AMG 386, or other molecules that inhibit the angiopoietins or Tie2 receptor
• Treatment within 30 days prior to randomization with strong immune modulators including but not limited to systemic cyclosporine, tacrolimus, sirolimus, mycophenolate mofetil, methotrexate, azathioprine, rapamycin, thalidomide, and lenalidomide
• Clinically significant cardiovascular disease within 12 months prior to randomization
• Major surgery within 28 days prior to randomization or still recovering from prior surgery
• Minor surgical procedures, except placement of tunneled central venous access device within 3 days prior to randomization. Diagnostic laparoscopy is regarded as a minor surgical procedure.