Large vision-language models (LVLMs) have demonstrated remarkable capabilities by integrating pre-trained vision encoders with large language models (LLMs). Similar to single-modal LLMs, chain-of-thought (CoT) prompting has been adapted for LVLMs to enhance multi-modal reasoning by generating intermediate rationales based on visual and textual inputs. While CoT is assumed to improve grounding and accuracy in LVLMs, our experiments reveal a key challenge: existing LVLMs often ignore the contents of generated rationales in CoT reasoning. To address this, we re-formulate multi-modal CoT reasoning as a KL-constrained reward maximization focused on rationale-conditional log-likelihood. As the optimal solution, we propose rationale-enhanced decoding (RED), a novel plug-and-play inference-time decoding strategy. RED harmonizes visual and rationale information by multiplying distinct image-conditional and rationale-conditional next token distributions. Extensive experiments show that RED consistently and significantly improves reasoning over standard CoT and other decoding methods across multiple benchmarks and LVLMs. Our work offers a practical and effective approach to improve both the faithfulness and accuracy of CoT reasoning in LVLMs, paving the way for more reliable rationale-grounded multi-modal systems. Code is available at https://github.com/yshinya6/red/.