The purposes of this study are to determine: 1) if treatment with interferon gamma-1b plus standard chemotherapy (carboplatin and paclitaxel) can increase the overall survival of patients with advanced ovarian or primary peritoneal carcinoma compared with chemotherapy alone; 2) how effective interferon gamma-1b plus standard chemotherapy is in preventing the progression or return of cancer; 3) the effects on quality of life; and 4) the safety of interferon gamma-1b combined with standard chemotherapy compared to chemotherapy alone.