Large language models often hallucinate, producing content that is factually incorrect or not grounded in the sources. Reliable faithfulness verification is critical for trustworthy deployment. In the provided-source (closed-world) setting, existing verifiers either classify whole passages in one step or check sentences independently, overlooking cross-sentence context. We present ContextCheck, a framework for sentence-level faithfulness verification with context-aware disambiguation. Each sentence is verified against the grounding document while conditioning on preceding sentences, enabling pronouns and references to be resolved directly in context. This design avoids the separate decontextualization step of rewriting claims into self-contained forms, casting verification as a context-conditioned task. Fine-tuned from Llama-3.1-8B-Instruct, ContextCheck sets a new state of the art on three context-dependent datasets; it improves Macro F1 by over 10 points compared to the strongest baselines, and matches or slightly surpasses the strongest baselines on 14 standard single-sentence datasets compared to prior 8B-scale verifiers (average Macro F1 73.5 vs. 72.8). These results show that ContextCheck offers a practical and effective approach for sentence-level hallucination detection.