The text generated by large language models is commonly controlled by prompting, where a prompt prepended to a user's query guides the model's output. The prompts used by companies to guide their models are often treated as secrets, to be hidden from the user making the query. They have even been treated as commodities to be bought and sold on marketplaces. However, anecdotal reports have shown adversarial users employing prompt extraction attacks to recover these prompts. In this paper, we present a framework for systematically measuring the effectiveness of these attacks. In experiments with 3 different sources of prompts and 11 underlying large language models, we find that simple text-based attacks can in fact reveal prompts with high probability. Our framework determines with high precision whether an extracted prompt is the actual secret prompt, rather than a model hallucination. Prompt extraction from real systems such as Claude 3 and ChatGPT further suggest that system prompts can be revealed by an adversary despite existing defenses in place.