Despite many stereotypes targeting intersectional demographic groups, prior studies on stereotypes within Large Language Models (LLMs) primarily focus on broader, individual categories. This research bridges this gap by introducing a novel dataset of intersectional stereotypes, curated with the assistance of the ChatGPT model and manually validated. Moreover, this paper offers a comprehensive analysis of intersectional stereotype propagation in three contemporary LLMs by leveraging this dataset. The findings underscore the urgency of focusing on intersectional biases in ongoing efforts to reduce stereotype prevalence in LLMs.