I. Determine the maximum tolerated dose (MTD), recommended phase II dose, dose limiting toxicity (DLT), and safety of ABT-888 (veliparib) with carboplatin and paclitaxel induction chemotherapy in locoregionally advanced head and neck (LAHNC) patients. (Phase I) II. Compare magnitude of tumor shrinkage (response) following 2 cycles of induction chemotherapy with and without ABT-888 in LAHNC. (Phase II)