This randomized phase II trial studies how well chemotherapy and radiation therapy given with or without metformin hydrochloride works in treating patients with stage III non-small cell lung cancer. Drugs used in chemotherapy, such as carboplatin and paclitaxel, work in different ways to stop the growth of tumor cells, either by killing the cells, by stopping them from dividing, or by stopping them from spreading. Radiation therapy uses high-energy x-rays to kill tumor cells and shrink tumors. Metformin hydrochloride may shrink tumors and keep them from coming back. It is not yet known whether chemotherapy and radiation therapy is more effective when given with or without metformin hydrochloride in treating stage III non-small cell lung cancer.