Large Language Models (LLMs) are shifting how scientific research is done. It is imperative to understand how researchers interact with these models and how scientific sub-communities like astronomy might benefit from them. However, there is currently no standard for evaluating the use of LLMs in astronomy. Therefore, we present the experimental design for an evaluation study on how astronomy researchers interact with LLMs. We deploy a Slack chatbot that can answer queries from users via Retrieval-Augmented Generation (RAG); these responses are grounded in astronomy papers from arXiv. We record and anonymize user questions and chatbot answers, user upvotes and downvotes to LLM responses, user feedback to the LLM, and retrieved documents and similarity scores with the query. Our data collection method will enable future dynamic evaluations of LLM tools for astronomy.