I. To establish the maximum tolerated dose (MTD) and the recommended phase II dose of ABT-888 (veliparib) when given concurrently with standard carboplatin/paclitaxel and radiotherapy in patients with unresectable stage III non-small cell lung cancer (NSCLC). (Phase I) II. To assess whether carboplatin/paclitaxel plus ABT-888 compared with carboplatin/paclitaxel plus placebo improves progression-free survival (PFS) in patients with unresectable stage III NSCLC. (Phase II) III. To compare overall survival (OS) in patients treated with carboplatin/paclitaxel and radiotherapy plus ABT-888 to those treated with carboplatin, paclitaxel and radiotherapy plus placebo. (Phase II) IV. To assess the response rate (confirmed and unconfirmed, complete and partial responses) and disease control rate in the subset of patients with measurable disease by Response Evaluation Criteria in Solid Tumors (RECIST) criteria. (Phase II) V. To assess the safety and toxicity profile of the regimen. (Phase II)