Smart contracts are susceptible to various security issues, among which access control (AC) vulnerabilities are particularly critical. While existing research has proposed multiple detection tools, the automatic and appropriate repair of AC vulnerabilities in smart contracts remains a challenge. Unlike commonly supported vulnerability types by existing repair tools, such as reentrancy, which are usually fixed by template-based approaches, the main obstacle of AC lies in identifying the appropriate roles or permissions amid a long list of non-AC-related source code to generate proper patch code, a task that demands human-level intelligence. Leveraging recent advancements in large language models (LLMs), we employ the state-of-the-art GPT-4 model and enhance it with a novel approach called ACFIX. The key insight is that we can mine common AC practices for major categories of code functionality and use them to guide LLMs in fixing code with similar functionality. To this end, ACFIX involves both offline and online phases. First, during the offline phase, ACFIX mines a taxonomy of common Role-based Access Control (RBAC) practices from 344,251 on-chain contracts, categorizing 49 role-permission pairs from the top 1,000 pairs mined. Second, during the online phase, ACFIX tracks AC-related elements across the contract and uses this context information along with a Chain-of-Thought pipeline to guide LLMs in identifying the most appropriate role-permission pair for the subject contract and subsequently generating a suitable patch. This patch will then undergo a validity and effectiveness check. To evaluate ACFIX, we built the first benchmark dataset of 118 real-world AC vulnerabilities, and our evaluation revealed that ACFIX successfully repaired 94.92% of them. This represents a significant improvement compared to the baseline GPT-4, which achieved only 52.54%.