Chest X-rays (CXRs) are the most frequently performed imaging examinations in clinical settings. Recent advancements in Large Multimodal Models (LMMs) have enabled automated CXR interpretation, enhancing diagnostic accuracy and efficiency. However, despite their strong visual understanding, current Medical LMMs (MLMMs) still face two major challenges: (1) Insufficient region-level understanding and interaction, and (2) Limited accuracy and interpretability due to single-step reasoning. In this paper, we empower MLMMs with anatomy-centric reasoning capabilities to enhance their interactivity and explainability. Specifically, we first propose an Anatomical Ontology-Guided Reasoning (AOR) framework, which centers on cross-modal region-level information to facilitate multi-step reasoning. Next, under the guidance of expert physicians, we develop AOR-Instruction, a large instruction dataset for MLMMs training. Our experiments demonstrate AOR's superior performance in both VQA and report generation tasks.