In recent years, large language models (LLMs) have seen rapid advancements, significantly impacting various fields such as computer vision, natural language processing, and software engineering. These LLMs, exemplified by OpenAI's ChatGPT, have revolutionized the way we approach language understanding and generation tasks. However, in contrast to traditional software development practices, LLM development introduces new challenges for AI developers in design, implementation, and deployment. These challenges span different areas (such as prompts, APIs, and plugins), requiring developers to navigate unique methodologies and considerations specific to LLM application development. Despite the profound influence of LLMs, to the best of our knowledge, these challenges have not been thoroughly investigated in previous empirical studies. To fill this gap, we present the first comprehensive study on understanding the challenges faced by LLM developers. Specifically, we crawl and analyze 29,057 relevant questions from a popular OpenAI developer forum. We first examine their popularity and difficulty. After manually analyzing 2,364 sampled questions, we construct a taxonomy of challenges faced by LLM developers. Based on this taxonomy, we summarize a set of findings and actionable implications for LLM-related stakeholders, including developers and providers (especially the OpenAI organization).