Despite significant technological advancements, the process of programming robots for adaptive assembly remains labor-intensive, demanding expertise in multiple domains and often resulting in task-specific, inflexible code. This work explores the potential of Large Language Models (LLMs), like ChatGPT, to automate this process, leveraging their ability to understand natural language instructions, generalize examples to new tasks, and write code. In this paper, we suggest how these abilities can be harnessed and applied to real-world challenges in the manufacturing industry. We present a novel system that uses ChatGPT to automate the process of programming robots for adaptive assembly by decomposing complex tasks into simpler subtasks, generating robot control code, executing the code in a simulated workcell, and debugging syntax and control errors, such as collisions. We outline the architecture of this system and strategies for task decomposition and code generation. Finally, we demonstrate how our system can autonomously program robots for various assembly tasks in a real-world project.