A Study to Assess the Efficacy and Safety of Farletuzumab (MORAb 003) in Combination With Carboplatin Plus Paclitaxel or Carboplatin Plus Pegylated Liposomal Doxorubicin (PLD) in Participants With Low CA125 Platinum-sensitive Ovarian Cancer

Inclusion Criteria: 1. Female subjects who are at least 18 years of age at the time of informed consent 2. CA125 less than or equal to 3 x upper limit of normal (ULN) \[105 units per millilitre (U/mL)\] confirmed within 2 weeks of randomization using a centralized laboratory assay 3. A histologically confirmed diagnosis of high-grade serous epithelial ovarian cancer including primary peritoneal and fallopian tube malignancies; all other histologies, including mixed histology, are excluded 4. Have been treated with debulking surgery and a first-line platinum-based chemotherapy regimen 5. Maintenance therapy during the first platinum-free interval is allowed; however, the last dose must have been at least 21 days prior to Randomization. 6. Must be in a first relapse and have evaluable disease by Computed Tomography (CT) or Magnetic Resonance Imaging (MRI) scan, according to RECIST 1.1 (subjects with measurable disease per RECIST 1.1 or radiographically visible and evaluable disease). Subjects with only ascites or pleural effusion are excluded. 7. Must have relapsed radiographically between 6 months and 36 months of completion of first-line platinum chemotherapy 8. Must be a candidate for treatment with either carboplatin plus paclitaxel or carboplatin plus PLD with no medical contraindications present as outlined in the product labels for the selected regimen to be used in this study 9. Have a life expectancy of at least 6 months, as estimated by the investigator 10. Other significant medical conditions must be well-controlled and stable in the opinion of the investigator for at least 30 days prior to Randomization 11. Have an Eastern Cooperative Oncology Group (ECOG) Performance Status 0-2 12. Subjects being enrolled to receive paclitaxel plus carboplatin treatment must have neuropathic function (sensory and motor less than or equal to Grade 2 according to the National Cancer Institute's Common Terminology Criteria for Adverse Events (CTCAE) v4.03 (2010) 13. Laboratory results within the 2 weeks prior to Randomization must be as follows: * Absolute neutrophil count (ANC) greater than or equal to 1.5 x 10\^9/L * Platelet count greater than or equal to 100 x 10\^9/L * Hemoglobin greater than or equal to 9 g/dL * Creatinine less than 1.5 x ULN (CTCAE Grade 1) * Bilirubin less than 1.5 x ULN (CTCAE Grade 1) * Aspartate Aminotransferase (AST) and Alanine Aminotransferase (ALT) less than 3 x ULN * Alkaline Phosphatase less than 2.5 x ULN (CTCAE Grade 1) * Baseline albumin greater than or equal to Lower Limit of Normal 14. Subjects of childbearing potential must be surgically sterile or consent to use a medically acceptable method of contraception throughout the study period. All females will be considered to be of childbearing potential unless they are postmenopausal (eg, amenorrheic for at least 12 consecutive months, in the appropriate age group, and without other known or suspected cause) or have been sterilized surgically (ie, bilateral tubal ligation, total hysterectomy, or bilateral oophorectomy, all with surgery at least 1 month before dosing). If a patient of childbearing potential is neither surgically sterile nor postmenopausal, a highly-effective contraceptive method (ie, a method that can achieve a failure rate of less than 1 percent (%) per year when used consistently and correctly) must start either before or at Screening and continue throughout the entire study period and for 6 months after the last dose of Test Article is administered. Pregnant and/or lactating females are excluded Exclusion Criteria: 1. Known central nervous system (CNS) tumor involvement 2. Evidence of other active invasive malignancy requiring treatment other than surgery in the past 3 years 3. Clinically significant heart disease (eg, congestive heart failure of New York Heart Association Class 3 or 4 angina, not well controlled by medication, or myocardial infarction within 6 months) 4. Electrocardiogram (ECG) demonstrating clinically significant arrhythmias that are not adequately medically managed (Note: subjects with chronic atrial arrhythmia, ie, atrial fibrillation or paroxysmal supraventricular tachycardia \[SVT\], are eligible) 5. Active serious systemic disease, including active bacterial or fungal infection 6. Active viral hepatitis or active human immunodeficiency virus (HIV) infection. Asymptomatic positive serology is not exclusionary. 7. Other concurrent immunotherapy (eg, immunosuppressants or chronic use of systemic corticosteroids, with the exception that low-dose corticosteroids \[50 mg/day prednisone or equivalent corticosteroid\] are allowed; these should be discussed with the Medical Monitor) 8. Known allergic reaction to a prior monoclonal antibody therapy or have any documented Anti-Drug Antibody (ADA) response; additionally known allergic reaction to the concomitant chemotherapies selected by the investigator for planned treatment in this study unless desensitization is planned 9. Previous treatment with farletuzumab or other folate receptor targeting agents 10. Previous treatment with cancer vaccine therapy 11. For subjects being enrolled to receive PLD plus carboplatin, prior treatment with anthracyclines or anthracenodiones 12. Breast-feeding, pregnant, or likely to become pregnant during the study 13. Any medical or other condition that, in the opinion of the investigator, would preclude the subject's participation in a clinical study including medical contraindications as outlined in the product labels for the chemotherapies selected by the investigator for planned treatment in this study 14. Patients who have had secondary debulking surgery or any second line therapy 15. Currently enrolled in another clinical study or used any investigational drug or device within 30 days (or 5 x half-life for investigational drugs where the half-life is known) preceding informed consent