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Molecule discovery plays a crucial role in various scientific fields, advancing the design of tailored materials and drugs. However, most of the existing methods heavily rely on domain experts, require excessive computational cost, or suffer from sub-optimal performance. On the other hand, Large Language Models (LLMs), like ChatGPT, have shown remarkable performance in various cross-modal tasks due to their powerful capabilities in natural language understanding, generalization, and in-context learning (ICL), which provides unprecedented opportunities to advance molecule discovery. Despite several previous works trying to apply LLMs in this task, the lack of domain-specific corpus and difficulties in training specialized LLMs still remain challenges. In this work, we propose a novel LLM-based framework (MolReGPT) for molecule-caption translation, where an In-Context Few-Shot Molecule Learning paradigm is introduced to empower molecule discovery with LLMs like ChatGPT to perform their in-context learning capability without domain-specific pre-training and fine-tuning. MolReGPT leverages the principle of molecular similarity to retrieve similar molecules and their text descriptions from a local database to enable LLMs to learn the task knowledge from context examples. We evaluate the effectiveness of MolReGPT on molecule-caption translation, including molecule understanding and text-based molecule generation. Experimental results show that compared to fine-tuned models, MolReGPT outperforms MolT5-base and is comparable to MolT5-large without additional training. To the best of our knowledge, MolReGPT is the first work to leverage LLMs via in-context learning in molecule-caption translation for advancing molecule discovery. Our work expands the scope of LLM applications, as well as providing a new paradigm for molecule discovery and design.