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

DISEASE CHARACTERISTICS: * Histologically confirmed ovarian epithelial, primary peritoneal, or fallopian tube cancer meeting 1 of the following criteria: * High-risk stage I disease, as defined by grade 3, aneuploid grade 1 or 2, or clear cell disease * Stage II, III, or IV disease * Completed first-line therapy within the past 6 weeks * Received a platinum derivative (carboplatin or cisplatin) alone or in combination with other agents for 6-9 courses * Must have achieved complete response/no evidence of disease, partial response, or stabilization of disease after therapy * No adenocarcinoma of unknown origin * No known brain metastases or leptomeningeal disease PATIENT CHARACTERISTICS: Performance status * ECOG 0-1 Life expectancy * Not specified Hematopoietic * Platelet count ≥ 100,000/mm\^3 * WBC ≥ 2,000/mm\^3 Hepatic * AST and ALT ≤ 2.5 times upper limit of normal (ULN) (≤ 5 times ULN in patients with known liver metastases) * Bilirubin ≤ 1.5 times ULN * Alkaline phosphatase ≤ 5 times ULN except in patients with known bone metastases * PT and PTT ≤ 1.5 times ULN Renal * Creatinine ≤ 2 times ULN Cardiovascular * No myocardial infarction within past 6 months * No second- or third-degree heart block without pacemaker Gastrointestinal * No active peptic ulcer disease * No gastrointestinal tract disease that would interfere with ability to take oral medications, affect absorption, or require parenteral nutrition * No uncontrolled inflammatory bowel disease (e.g., Crohn's disease or ulcerative colitis) Other * Not pregnant or nursing * Negative pregnancy test * Fertile patients must use effective contraception * No significant dermatologic disease * No inflammatory changes to the surface of the eye * No history of allergic reaction to compounds of similar chemical composition as erlotinib * No other significant medical condition or neurologic or psychiatric disorder * No other malignancy within the past 5 years except adequately treated basal cell or squamous cell skin cancer or cone-biopsied carcinoma in situ of the cervix * No psychiatric illness or familial, geographic, or social situation that would preclude study compliance PRIOR CONCURRENT THERAPY: Biologic therapy * No prior therapy targeting epidermal growth factor receptor * No concurrent immunotherapy Chemotherapy * See Disease Characteristics * See Surgery * No concurrent chemotherapy Endocrine therapy * No concurrent hormonal therapy Radiotherapy * No prior radiotherapy unless completed more than 5 years ago AND outside the abdomen/pelvis Surgery * Interval debulking surgery after 3 courses of chemotherapy and second-look surgery at the end of chemotherapy allowed as per study EORTC-55971/NCIC OV13/Chorus Other * No other prior or concurrent investigational agents * No other concurrent anticancer treatment * Concurrent participation in study EORTC-55971/NCIC-OV13/Chorus allowed