Given the importance of identifying and monitoring news stories within the continuous flow of news articles, this paper presents PromptStream, a novel method for unsupervised news story discovery. In order to identify coherent and comprehensive stories across the stream, it is crucial to create article representations that incorporate as much topic-related information from the articles as possible. PromptStream constructs these article embeddings using cloze-style prompting. These representations continually adjust to the evolving context of the news stream through self-supervised learning, employing a contrastive loss and a memory of the most confident article-story assignments from the most recent days. Extensive experiments with real news datasets highlight the notable performance of our model, establishing a new state of the art. Additionally, we delve into selected news stories to reveal how the model’s structuring of the article stream aligns with story progression.