Gemcitabine will be administered by intravenous infusion of 1000 mg/m2 over 30 minutes on days 1, 8, 15 of the cycle. Intensity modulated radiation therapy (IMRT) will be given to a total dose of 36 Gy in 15 fractions (2.4 Gy per fraction, one fraction per day, 5 fractions per week, Monday through Friday) beginning on day 1. Veliparib will be administered per a dose escalation schema. The starting dose of veliparib is 20 mg BID based upon safety/efficacy data available. Dose escalation will continue in 20 mg increments until the maximum tolerated dose (MTD) is reached. Intra-patient dose escalation will not be allowed.