Developing and training deep learning models is expensive, so software engineers have begun to reuse pre-trained deep learning models (PTMs) and fine-tune them for downstream tasks. Despite the widespread use of PTMs, we know little about the corresponding software engineering behaviors and challenges. To enable the study of software engineering with PTMs, we present the PeaTMOSS dataset: Pre-Trained Models in Open-Source Software. PeaTMOSS has three parts: a snapshot of (1) 281,638 PTMs, (2) 27,270 open-source software repositories that use PTMs, and (3) a mapping between PTMs and the projects that use them. We challenge PeaTMOSS miners to discover software engineering practices around PTMs. A demo and link to the full dataset are available at: https://github.com/PurdueDualityLab/PeaTMOSS-Demos.