Conventional wisdom holds that open, collaborative, and transparent organizations are innovative. But some of the most radical innovations—satellites, lithium-iodine batteries, the internet—were conceived by small, secretive teams in national security agencies. Are these organizations more innovative because of their secrecy, or in spite of it? We study a principal–agent model of public-sector innovation. We give research teams a secret option and a public option during the initial testing and prototyping phase. Secrecy helps advance high-risk, high-reward projects through the early phase via a cost-passing mechanism. In open institutions, managers will not approve pilot research into high-risk, high-reward ideas for fear of political costs. Researchers exploit secrecy to conduct pilot research at a higher personal cost to generate evidence that their project is viable and win their manager's approval. Contrary to standard principal–agent findings, we show that researchers may exploit secrecy even if their preferences are perfectly aligned with their manager's, and that managers do not monitor researchers even if monitoring is costless and perfect. We illustrate our theory with two cases from the early Cold War: the CIA's attempt to master mind control (MKULTRA) and the origins of the reconnaissance satellite (CORONA). We contribute to the political application of principal–agent theory and studies of national security innovation, emerging technologies, democratic oversight, the Sino–American technology debate, and great power competition.