Index recommendation is crucial for optimizing database performance. However, existing heuristic- and learning-based methods often rely on inefficient exhaustive search and estimated costs, leading to low efficiency (due to the vast search space) and unsatisfactory actual latency (due to inaccurate estimations). Inspired by the refinement strategies of experienced DBAs-who efficiently identify and iteratively refine indexes with database feedback-we present LLMIA, an out-of-the-box, tuning-free index advisor leveraging large language models (LLMs) through in-context learning for index recommendation. LLMIA injects database expertise into the LLM using a high-quality demonstration pool and comprehensive workload feature extraction, while iteratively incorporating database feedback to guide the index refinement. This design enables LLMIA to emulate the decision-making process of expert DBAs: efficiently recommending and refining indexes for various workloads within just a few interactions with the DBMS. We validate LLMIA with extensive experiments on five standard OLAP benchmarks (TPC-H with different scales, JOB, TPC-DS, SSB), where it consistently outperforms or matches 12 baselines by producing superior index recommendations with minimal database interactions. Additionally, LLMIA demonstrates robust generalization on two real-world commercial workloads, delivering high-quality recommendations without the need for additional adaptation or retraining, highlighting its out-of-the-box capability.

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