TRINOVA-1: A Study of AMG 386 or Placebo, in Combination With Weekly Paclitaxel Chemotherapy, as Treatment for Ovarian Cancer, Primary Peritoneal Cancer and Fallopian Tube Cancer

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.