 In this study, participants will take ZD1839 by mouth daily. Once the treatment has started, participants will return to the clinic before every treatment cycle every 4 weeks for the first 4 months then every 8 weeks thereafter. At these visits, participants will have a physical exam and blood tests will be performed. About 2-4 teaspoons of blood will be drawn at each visit. The doctor will also check on how participants are tolerating ZD1839 side effects. Every 8 weeks, participants will have their tumor evaluated by radiographic scans. This may include either a CT or MRI and a chest X-ray. 