Large Language Models generate complex reasoning chains that reveal their decision-making, yet verifying the faithfulness and harmlessness of these intermediate steps remains a critical unsolved problem. Existing auditing methods are centralized, opaque, and hard to scale, creating significant risks for deploying proprietary models in high-stakes domains. We identify four core challenges: (1) Robustness: Centralized auditors are single points of failure, prone to bias or attacks. (2) Scalability: Reasoning traces are too long for manual verification. (3) Opacity: Closed auditing undermines public trust. (4) Privacy: Exposing full reasoning risks model theft or distillation. We propose TRUST, a transparent, decentralized auditing framework that overcomes these limitations via: (1) A consensus mechanism among diverse auditors, guaranteeing correctness under up to $30\%$ malicious participants. (2) A hierarchical DAG decomposition of reasoning traces, enabling scalable, parallel auditing. (3) A blockchain ledger that records all verification decisions for public accountability. (4) Privacy-preserving segmentation, sharing only partial reasoning steps to protect proprietary logic. We provide theoretical guarantees for the security and economic incentives of the TRUST framework. Experiments across multiple LLMs (GPT-OSS, DeepSeek-r1, Qwen) and reasoning tasks (math, medical, science, humanities) show TRUST effectively detects reasoning flaws and remains robust against adversarial auditors. Our work pioneers decentralized AI auditing, offering a practical path toward safe and trustworthy LLM deployment.