Automatic taxonomy induction is crucial for web search, recommendation systems, and question answering. Manual curation of taxonomies is expensive in terms of human effort, making automatic taxonomy construction highly desirable. In this work, we introduce Chain-of-Layer which is an in-context learning framework designed to induct taxonomies from a given set of entities. Chain-of-Layer breaks down the task into selecting relevant candidate entities in each layer and gradually building the taxonomy from top to bottom. To minimize errors, we introduce the Ensemble-based Ranking Filter to reduce the hallucinated content generated at each iteration. Through extensive experiments, we demonstrate that Chain-of-Layer achieves state-of-the-art performance on four real-world benchmarks.