PHASE I: Patients receive veliparib orally (PO) twice daily (BID) on days 1-7, paclitaxel intravenously (IV) over 60 minutes on days 1, 8, and 15, and carboplatin IV over 30 minutes on day 1. Treatment repeats every 3 weeks for 2 courses in the absence of disease progression or unacceptable toxicity. Patients then continue on to concomitant chemoradiotherapy.