A Study of Vismodegib (GDC-0449, Hedgehog Pathway Inhibitor) As Maintenance Therapy in Patients With Ovarian Cancer in a Second or Third Complete Remission

Inclusion Criteria: * Histologic diagnosis of epithelial ovarian carcinoma, primary peritoneal carcinoma, or fallopian tube carcinoma * Must be in second or third complete remission, have received chemotherapy (platinum-based and/or non-platinum-based) for recurrent disease, and have achieved a complete remission after their most recent chemotherapy regimen. Complete remission is defined as no symptoms suggestive of persistent cancer, computed tomography (CT) scan of the chest/abdomen/pelvis without evidence of ovarian cancer within 4 weeks of randomization, and normal CA-125 (measured within 2 weeks of randomization) following completion of prior chemotherapy. The study investigator should confirm the status of disease remission by CT scan before patient enrollment. If patient has lymphadenopathy by CT scan and the investigator thinks that it is unlikely due to ovarian cancer, this patient is considered eligible. If indicated, a confirmatory biopsy should be performed. * Patients must have completed their most recent cytotoxic chemotherapy regimen (platinum-based or non-platinum based) no less than 3 weeks and no more than 14 weeks prior to randomization. * Archival tissue must be available and requested. * Negative pregnancy test on Day 1 (first day the patient receives vismodegib or placebo). * For women of childbearing potential: Use of two effective methods of contraception, including one barrier method. Exclusion Criteria: * Pregnancy or lactation. * Patients whose ovarian cancer is in first remission. * Patients must not have experienced more than two prior recurrences of disease. * Concurrent non-protocol-specified anti-tumor therapy, either approved or unapproved (eg, chemotherapy, hormonal therapy, other targeted therapy, radiation therapy, surgery, herbal therapy). Hormonal replacement therapies for treatment of postmenopausal symptoms do not exclude patients from this study. * Current, recent (within 4 weeks of Day 1), or planned participation in an experimental drug study while enrolled in this study. * History of other malignancies within 3 years of Day 1, except for tumors with a negligible risk for metastasis or death, such as adequately treated basal cell carcinoma (BCC) or squamous-cell carcinoma of the skin; ductal carcinoma in situ of the breast; or carcinoma in situ of the cervix. * Uncontrolled medical illnesses such as infection requiring intravenous (IV) antibiotics. * Life expectancy \< 12 weeks. * History of other disease, metabolic dysfunction, physical examination finding, or clinical laboratory finding giving reasonable suspicion of a disease or condition that contraindicates use of an investigational drug or that might affect interpretation of the results of the study or render the patient at high risk from treatment complications.