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 wide-spread 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.