Recent advancements in conversational large language models (LLMs), such as ChatGPT, have demonstrated remarkable promise in various domains, including drug discovery. However, existing works mainly focus on investigating the capabilities of conversational LLMs on chemical reactions and retrosynthesis. While drug editing, a critical task in the drug discovery pipeline, remains largely unexplored. To bridge this gap, we propose ChatDrug, a framework to facilitate the systematic investigation of drug editing using LLMs. ChatDrug jointly leverages a prompt module, a retrieval and domain feedback module, and a conversation module to streamline effective drug editing. We empirically show that ChatDrug reaches the best performance on all 39 drug editing tasks, encompassing small molecules, peptides, and proteins. We further demonstrate, through 10 case studies, that ChatDrug can successfully identify the key substructures for manipulation, generating diverse and valid suggestions for drug editing. Promisingly, we also show that ChatDrug can offer insightful explanations from a domain-specific perspective, enhancing interpretability and enabling informed decision-making.