This is a Phase II study of paclitaxel administered as a 96-hour (4 day) continuous infusion with a bolus of cisplatin followed by chest radiotherapy for previously untreated patients with stage III non-small cell lung cancer (NSCLC). The non-small cell lung cancer tissue obtained prior to the start of treatment will be studied for mutations of the p53 gene. The goal of this phase II study is to determine the response rate to 4 cycles of infusional paclitaxel and bolus cisplatin for patients with stage III NSCLC. The response will again be assessed following completion of 6000 cGy of chest radiotherapy and the patients will then be followed for survival. The relationship between the presence or absence of a p53 mutation and the sensitivity of the patient's tumors to paclitaxel plus cisplatin and chest radiation will be studied. In addition, the plasma levels of paclitaxel will be measured, and the in vitro paclitaxel chemosensitivity of the tumor cells will be determined from as many patients as possible. This will allow further study of the relationship between p53 status, in vitro drug sensitivity, achievable plasma concentrations of paclitaxel, and patients' response to therapy.