Abstract: Chart reasoning agents are increasingly used to extract actionable insights in critical domains, achieving state-of-the-art performance on multiple benchmarks. Yet, high benchmark accuracy alone is insufficient for deployment, where stakeholders must be able to audit and verify how a model reaches its answer. Existing LVLM-based chart agents produce either answer-only predictions or free-form rationales that are hard to verify, obscuring whether an error arose from misreading the chart, extracting a wrong value, or miscomputing. We propose Chart-RVR, a reinforcement learning framework for training monitorable chart agents with verifiable process rewards. Chart-RVR decomposes chart reasoning into three auditable blocks: Structure, identifying the chart type; Evidence, reconstructing the underlying data table in JSON; and Derivation, exposing the stepwise trace that computes the answer. Across six in-domain and out-of-domain benchmarks, Chart-RVR attains state-of-the-art accuracy among comparable-sized LVLMs. Beyond accuracy, we assess monitorability using a triangulated protocol that combines ground-truth surrogate metrics, an oracle information-gain measure, and an LLM-as-auditor scoring Process Verifiability and Evidence Localization, showing that Chart-RVR yields rationales that are markedly more verifiable and evidence-grounded than those from CoT prompting, SFT, and existing chart-specific baselines.