The purpose of this study is to determine if an investigational cell therapy called Cvac can help epithelial ovarian cancer (EOC) from returning when administered to patients who are in complete remission after surgical removal of their tumor followed by standard first-line (Part A) or second-line (Part B) chemotherapy. Following remission, patients will undergo leukapheresis for the manufacture of the study agent. After completion of chemotherapy and confirmation of remission, patients will enter the treatment phase of the study.