OUTLINE: This is nonrandomized study. Chemotherapy on cycle 1 starts on day 1 with concurrent initiation of radiotherapy. Chemotherapy is given prior to radiotherapy on those days when both treatments are given. Cycle 2 begins on day 29. Carboplatin is administered by 15 minute IV infusions on days 1, 3, 29, and 31. Etoposide (VP-16) is administered after carboplatin by 30 minute IV infusions on days 1-4, and 29-32. Radiation therapy begins within 24 hours of day 1, cycle 1 of chemotherapy. The primary tumor, the adjacent mediastinum, and other targeted lymph nodes are administered radiotherapy daily 5 days a week for 6.5 weeks. After the 2 cycles of chemotherapy and chest radiotherapy, patients who have stable disease, partial response, or complete response receive 3 cycles of paclitaxel. Paclitaxel is administered by 3 hour IV infusions starting 4 weeks after completion of chemotherapy and radiotherapy and repeated every 3-4 weeks (approximately days 71, 92, and 103) for a total of 3 cycles. Patients are followed every month for the first year, every 3 months for the second year, every 6 months for the third year, and then annually thereafter while on treatment. After treatment, patients are followed every 6 months for 2 years and then annually thereafter.