The widespread death and disruption caused by COVID-19 pandemic has revealed the failure of existing institutions to protect the health and well-being of humanity. Lack of accurate and timely data along with pervasive misinformation is causing even more harm and growing tension between data privacy and public health concerns.This paper describes how blockchain, with its distributed trust networks and cryptography-based security, may provide solutions to some of these data-related trust problems.Blockchain is being applied in innovative ways that are relevant to the current COVID-19 crisis. We describe examples of the challenges in existing technologies to track medical supplies and infected patients and how blockchain technology applications may help in these situations.This review of existing and potential applications of blockchain technology for medical care show how its distributed governance structure and privacy preserving features may create a "trustless" system that helps resolve the tension between privacy and public health needs in the fight against COVID-19.Blockchain relies on a distributed, robust, secure, privacy-preserving, and immutable record framework that can transform the nature of trust, value sharing, and transactions for the better. A nationally coordinated effort to explore blockchain for addressing the failures of existing systems and a partnership of academia, researchers, business, and industry is suggested to expedite the adoption of blockchain in healthcare.