Molecular property prediction is fundamental to drug discovery and materials science, yet existing models suffer from limited interpretability and poor cross-task generalization. Without explainable chemical rationales, accurate predictions alone are insufficient for guiding costly downstream experiments. We propose MppReasoner, a multimodal large language model that incorporates verifiable chemical reasoning for molecular property prediction. Built on Qwen2.5-VL-7B-Instruct, MppReasoner integrates 2D molecular images with SMILES strings through a two-stage training strategy: supervised fine-tuning (SFT) on 16,000 expert-guided reasoning trajectories, followed by Reinforcement Learning from Principle-Guided Rewards (RLPGR). RLPGR applies rule-based rewards verified by RDKit to evaluate chemical principle usage, structural analysis, and logical consistency, providing objective feedback without human preference labels. Experiments across 8 benchmark datasets show that MppReasoner outperforms the strongest baseline by 2.95% and 5.49% on in-distribution and out-of-distribution tasks, respectively. Beyond predictive accuracy, MppReasoner generates chemically grounded reasoning traces, with expert evaluation confirming high reasoning quality across three assessed dimensions. Code is available at https://github.com/Jesse-zjx/MPPReasoner.