Humanitarian aid-distribution programs help bring physical goods to people in need. Traditional paper-based solutions to support aid distribution do not scale to large populations and are hard to secure. Existing digital solutions solve these issues, at the cost of collecting large amount of personal information. This lack of privacy can endanger recipients' safety and harm their dignity. In collaboration with the International Committee of the Red Cross, we build a safe digital aid-distribution system. We first systematize the requirements such a system should satisfy. We then propose a decentralized solution based on the use of tokens that fulfills the needs of humanitarian organizations. It provides scalability and strong accountability, and, by design, guarantees the recipients' privacy. We provide two instantiations of our design, on a smart card and on a smartphone. We formally prove the security and privacy properties of these solutions, and empirically show that they can operate at scale.