Paclitaxel + Carboplatin With AVB-S6-500 in Women With Stage III or IV Epithelial Ovarian, Primary Peritoneal, or Fallopian Tube Cancer Receiving Neoadjuvant Chemotherapy

Inclusion Criteria: * Histologic diagnosis of epithelial ovarian, fallopian tube, or primary peritoneal cancer per pre-treatment biopsies by laparoscopy or interventional radiology or CT-guided core biopsy. * Patients with the following histologic epithelial cell types are eligible: * High grade serous adenocarcinoma * Endometrioid adenocarcinoma * Undifferentiated carcinoma * Clear cell adenocarcinoma * Mixed epithelia carcinoma * Adenocarcinoma not otherwise specified (NOS) * Disease must be considered "bulky" by the clinician (unresectable via primary debulking surgery) and in need of neoadjuvant chemotherapy prior to debulking surgery. This assessment of unresectability can be made via imaging or laparoscopic scoring. * Must have pre-treatment tumor tissue available or agree to tissue collection from IR-guided biopsy. * Any hormonal therapy directed at the malignant tumor must be discontinued at least one week prior to registration. Continuation of hormone replacement therapy is permitted. * At least 18 years of age. * Eastern Cooperative Oncology Group (ECOG) performance status ≤ 2 * Normal bone marrow and organ function as defined below: * Absolute neutrophil count ≥ 1,500/mcl * Platelets ≥ 100,000/mcl * Hemoglobin ≥ 9.0 g/dL * Total bilirubin ≤ 1.5 x IULN * AST(SGOT)/ALT(SGPT) ≤ 2.5 x IULN (unless liver metastases are present in which case AST/ALT must be ≤ 5.0 x IULN) * Serum creatinine \< 2.0 mg/dL or \< 177 µmol/L OR calculated or measured creatinine clearance ≥ 40 mL/min (using Cockcroft-Gault equation) * INR ≤ 1.5 x IULN * aPTT ≤ 1.5 x IULN * Women of childbearing potential must agree to use adequate contraception (hormonal or barrier method of birth control, abstinence) prior to study entry and for the duration of study participation. Should a woman become pregnant or suspect she is pregnant while participating in this study, she must inform her treating physician immediately. * Ability to understand and willingness to sign an IRB approved written informed consent document (or that of legally authorized representative, if applicable). Exclusion Criteria: * Any prior treatment with AVB-S6-500 or standard of care drugs (cisplatin, carboplatin, paclitaxel). * A history of other malignancy ≤ 3 years previous with the exception of basal cell or squamous cell carcinoma of the skin which were treated with local resection only. Patients with concomitant endometrial cancer diagnosed at the time of the ovarian cancer are allowed to participate if the endometrial cancer is FIGO stage IB or less. * Currently receiving any other (non-study) cytotoxic chemotherapy. * Currently receiving any other investigational agents or has received an investigational agent within 4 weeks of start of study treatment. * Known brain metastases. Patients with known brain metastases must be excluded from this clinical trial because of their poor prognosis and because they often develop progressive neurologic dysfunction that would confound the evaluation of neurologic and other adverse events. * A history of allergic reactions attributed to compounds of similar chemical or biologic composition to AVB-S6-500 or other agents used in the study. * Abnormal gastrointestinal function (nausea or vomiting). This includes GI obstruction or bleeding or signs/symptoms thereof within 3 months of study enrollment. Patients with a history of abdominal fistula will be considered eligible if the fistula was surgically repaired or has healed, there has been no evidence of fistula for at least 6 months, and patient is deemed to be at low risk of recurrent fistula. * Significant cardiac disease history including: * Clinically significant atrial or ventricular arrhythmias requiring treatment * Medically controlled congestive heart failure * Significant angina or clinically and/or electrocardiographically documented myocardial infarction within the past year * Clinically significant valvular disease * Non-healing wound, ulcer, or bone fracture. * Receiving treatment for active autoimmune disease. "Active" refers to any condition currently requiring therapy. * Received prior radiotherapy to any portion of the abdominal cavity or pelvis. Prior radiation for localized cancer of the breast, head and neck, or skin is permitted, provided that it was completed more than 3 years prior to registration and the patient remains free of recurrent or metastatic disease. * Received prior chemotherapy for any abdominal or pelvic tumor. Prior adjuvant chemotherapy for localized breast cancer is permitted, provided that was completed more than 3 years prior to registration and the patient remains free of recurrent or metastatic disease. * Known active hepatitis; ongoing systemic bacterial, fungal, or viral infection; known HIV infection or AIDS-related illness. * History or evidence upon physical examination of CNS disease, including primary brain tumor, seizures not controlled with standard medical therapy, or history of CVA, TIA, or subarachnoid hemorrhage within 6 months of the first date of treatment on this study. * Uncontrolled intercurrent illness including, but not limited to, ongoing or active infection, symptomatic congestive heart failure, unstable angina pectoris, or cardiac arrhythmia. * History of major surgical procedure within 21 days prior to start of study treatment. * Pregnant and/or breastfeeding. Women of childbearing potential must have a negative pregnancy test within 14 days of study entry.