This paper introduces a framework that leverages Large Language Models (LLMs) to answer natural language queries about General Transit Feed Specification (GTFS) data. The framework is implemented in a chatbot called TransitGPT with open-source code. TransitGPT works by guiding LLMs to generate Python code that extracts and manipulates GTFS data relevant to a query, which is then executed on a server where the GTFS feed is stored. It can accomplish a wide range of tasks, including data retrieval, calculations, and interactive visualizations, without requiring users to have extensive knowledge of GTFS or programming. The LLMs that produce the code are guided entirely by prompts, without fine-tuning or access to the actual GTFS feeds. We evaluate TransitGPT using GPT-4o and Claude-3.5-Sonnet LLMs on a benchmark dataset of 100 tasks, to demonstrate its effectiveness and versatility. The results show that TransitGPT can significantly enhance the accessibility and usability of transit data.