Outcomes After Secondary Cytoreductive Surgery With or Without Carboplatin Hyperthermic Intraperitoneal Chemotherapy (HIPEC) Followed by Systemic Combination Chemotherapy for Recurrent Platinum-Sensitive Ovarian, Fallopian Tube, or Primary Peritoneal Cancer

Inclusion Criteria: Inclusion Criteria for Eligibility Prior to Surgery: * Age ≥ 21 years old. * Patients with histologic diagnosis of epithelial ovarian carcinoma, primary peritoneal carcinoma, or fallopian tube carcinoma that has recurred \>6 months since platinum-based chemotherapy (first recurrence) and who are scheduled for secondary surgical evaluation/cytoreduction. * Histologic epithelial cell types include serous, endometrioid, clear cell, or undifferentiated carcinomas, transitional cell carcinoma, mixed epithelial carcinoma, malignant Brenner's tumor, or adenocarcinoma N.O.S. * Karnofsky Performance Status (KPS) of ≥ 70%. * Disease-free interval ≤ 30 months. * No prior chemotherapy in the recurrent setting. Prior hormonal therapy is permitted. Concomitant anti-neoplastic anti-hormonal therapy (including tamoxifen, aromatase inhibitors etc.) is not allowed for patients participating in study treatment. Low-dose (physiologic) estrogen hormone-replacement therapy (HRT) may be given. * Patients receiving maintenance biologic therapy are eligible, provided their recurrence is documented more than 6 months from completion of primary cytotoxic chemotherapy (includes maintenance chemotherapy) and a minimum of 3 weeks has elapsed since their last infusion of biologic therapy at the start of protocol intervention, day 1. * Patients must be, after evaluation by the investigator, appropriate candidates for the administration of 5 to 6 cycles of standard platinum-based combination chemotherapy (carboplatin and paclitaxel, carboplatin and liposomal doxorubicin, or carboplatin and gemcitabine) following CRS with or without HIPEC. * Bone marrow function: * Hemoglobin ≥ 8.5 g/dL. * Absolute neutrophil count (ANC) ≥ 1,000/mm3. * Platelets ≥ 100,000/mm3. * Renal function: * Creatinine ≤ 1.5mg/dl * Hepatic function: * Bilirubin ≤ 1.5 times ULN. * ALT ≤ 3 times the ULN. * AST ≤ 3 times the ULN. * Neurologic function: * Peripheral neuropathy ≤ CTC AE grade 2. * Blood coagulation parameters: * PT with an INR of ≤ 1.5 and a PTT ≤ 1.5 times the ULN. For patients on full-dose oral anti-coagulation (such as warfarin or rivaroxaban), in-range INR (usually between 2 and 3) and a PTT \<1.2 times the ULN. * Patients of childbearing potential must have a negative serum pregnancy test within 2 weeks prior to CRS and must be practicing an effective form of contraception during the study period. Inclusion Criteria for Eligibility Post-Surgery: * Patients will be consented prior to the surgical evaluation/cytoreductive surgery. Patients must have less than or equal to 0.5cm residual disease at the completion of the secondary surgery to be eligible for the study. Exclusion Criteria: Exclusion Criteria for Eligibility Prior to Surgery: * Tumors of low malignant potential (borderline carcinomas). * Subjects who have received prior radiotherapy to any portion of the abdominal cavity or pelvis are excluded. * Patients with a history of primary endometrial cancer are excluded unless the following conditions are met: * Stage not greater than IA. * Not a poorly differentiated subtype (including papillary serous, clear cell or other FIGO grade 3 lesions) * With the exception of non-melanoma skin cancer and other specific malignancies as noted above, subjects with other invasive malignancies, who had any evidence of the other cancer present within the last 1 year or whose previous cancer treatment contraindicates this protocol therapy, are excluded. * Subjects with known active acute hepatitis. * Subjects with active infection that requires parenteral antibiotics. * Active coronary artery disease (defined as unstable angina or a positive cardiac stress test). * Patients with a history of coronary artery disease may be included if they have had a normal stress test within 30 days of enrollment. * Uncontrolled hypertension defined as \> 140/90 and not cleared for surgery at the time of consent.. * New York Heart Association (NYHA) Class II or higher Congestive heart failure. * History of cerebrovascular disease. * Immune deficiency: Clinically significant primary or acquired immune deficiency (i.e. AIDS or on immunosuppressive medication after organ transplant). * Patients with other concurrent severe medical problems unrelated to the malignancy that would significantly limit full compliance with the study or places them at an unacceptable risk for participation in the study. * Patients with known carboplatin or cisplatin allergy. * Life expectancy \< 12 weeks. Exclusion Criteria for Eligibility Post-Surgery: * Evidence of extensive intraperitoneal adhesions at the time of surgery, as determined by the operating surgeon which prohibits intraperitoneal therapy.