The purpose of this study is to test the efficacy and safety of an experimental drug, OMP-305B83, when given in combination with paclitaxel. OMP-305B83 is a humanized monoclonal antibody and was developed to target cancer stem cells. Based on preclinical studies, it is believed that OMP-305B83 may block the growth of cancer stem cells and may also impair the productive growth of new blood vessels, which tumors need to grow and spread.

This is an open-label, Phase 1b dose escalation and expansion study of OMP-305B83 plus paclitaxel designed to evaluate the safety, efficacy and pharmacokinetics of OMP-305B83 in combination with paclitaxel in patients with platinum resistant ovarian, primary peritoneal or fallopian tube cancer. This study consists of a screening period, a treatment period and a post-treatment follow up period in which patients will be followed for survival for approximately 12 months. Patients will be enrolled in two stages: a dose-escalation stage and an expansion phase.

Approximately 30 patients will be enrolled in this study at approximately 5 study centers in the United States (U.S)..

Inclusion Criteria:

1. Platinum resistant Grade 2 or 3 ovarian, primary peritoneal or fallopian tube cancer
2. Measureable disease per response evaluation criteria (RECIST) v1.1
3. Prior bevacizumab
4. Age > or = 21 years
5. Adequate organ and marrow function
6. For women of childbearing potential and men with partners of childbearing potential, agreement (by patient and/or partner) to use two effective forms of contraception from study entry through at least 6 months after the termination visit.
7. Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

1. Treatment with any anti-cancer therapy, including radiotherapy, chemotherapy, biologic therapy. Prior therapy with weekly paclitaxel for recurrent disease, unless administered more than 2 years prior to enrollment, unless part of an upfront treatment strategy.
2. History of abdominal fistula, gastrointestinal perforation, intra-abdominal abscess, clinical signs or symptoms of gastrointestinaI obstruction or other known clinically signification gastrointestinal disease.
3. Subjects with brain metastases
4. Subjects with leptomeningial disease or neoplasms in the last 5 years
5. Blood pressure >140/80
6. Significant intercurrent illness that will limit the patient's ability to participate in the study
7. Subjects with known metastases that are currently involving the lumen of the gastrointestinal tract.
8. Major surgical procedure, open biopsy, or significant traumatic injury within 28 days prior to enrollment, or anticipation of need for major surgical procedure during the course of the study
9. Pregnant or nursing women
10. New York Heart Association Classification II, III, or IV
11. Inability to comply with study and follow up procedure