 This phase II trial is studying the side effects of giving erlotinib together with carboplatin and paclitaxel and to see how well it works in treating patients with stage III or stage IV ovarian, fallopian tube, or primary peritoneal cancer. Biological therapies such as erlotinib may interfere with the growth of tumor cells and slow the growth of the tumor. Drugs used in chemotherapy such as carboplatin and paclitaxel use different ways to stop tumor cells from dividing so they stop growing or die. 