Erlotinib or Observation in Treating Patients Who Have Undergone First-Line Chemotherapy for Ovarian Cancer, Peritoneal Cancer, or Fallopian Tube Cancer

RATIONALE: Erlotinib may stop the growth of tumor cells by blocking some of the enzymes needed for cell growth. Sometimes after treatment, the tumor may not need additional treatment until it progresses. In this case, observation may be sufficient. It is not yet known whether erlotinib is more effective than observation after first-line chemotherapy in treating patients with ovarian cancer, peritoneal cancer, or fallopian tube cancer. PURPOSE: This randomized phase III trial is studying erlotinib to see how well it works compared to observation in treating patients who have undergone first-line chemotherapy for ovarian cancer, peritoneal cancer, or fallopian tube cancer.