Open intent detection, a crucial aspect of natural language understanding, involves the identification of previously unseen intents in user-generated text. Despite the progress made in this field, challenges persist in handling new combinations of language components, which is essential for compositional generalization. In this paper, we present a case study exploring the use of ChatGPT as a data augmentation technique to enhance compositional generalization in open intent detection tasks. We begin by discussing the limitations of existing benchmarks in evaluating this problem, highlighting the need for constructing datasets for addressing compositional generalization in open intent detection tasks. By incorporating synthetic data generated by ChatGPT into the training process, we demonstrate that our approach can effectively improve model performance. Rigorous evaluation of multiple benchmarks reveals that our method outperforms existing techniques and significantly enhances open intent detection capabilities. Our findings underscore the potential of large language models like ChatGPT for data augmentation in natural language understanding tasks.