Patients receive gemcitabine intravenously (IV) over 30 minutes on days 1 and 8 and cisplatin IV over 1 hour on day 1. Patients also receive gefitinib orally (PO) once daily (QD) beginning on day 1. Treatment repeats every 21 days for up to 6 courses in the absence of disease progression or unacceptable toxicity. Patients who achieve complete remission, partial remission, or maintain stable disease continue gefitinib PO QD for 5 years or until disease progression or unacceptable toxicity occurs.