The widespread death and disruption caused by the COVID-19 pandemic has revealed deficiencies of existing institutions regarding the protection of human health and well-being. Both a lack of accurate and timely data and pervasive misinformation are causing increasing harm and growing tension between data privacy and public health concerns.This aim of this paper is to describe how blockchain, with its distributed trust networks and cryptography-based security, can provide solutions to 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 faced by existing technologies to track medical supplies and infected patients and how blockchain technology applications may help in these situations.This exploration of existing and potential applications of blockchain technology for medical care shows how the distributed governance structure and privacy-preserving features of blockchain can be used to create "trustless" systems that can help resolve the tension between maintaining privacy and addressing public health needs in the fight against COVID-19.Blockchain relies on a distributed, robust, secure, privacy-preserving, and immutable record framework that can positively transform the nature of trust, value sharing, and transactions. A nationally coordinated effort to explore blockchain to address the deficiencies of existing systems and a partnership of academia, researchers, business, and industry are suggested to expedite the adoption of blockchain in health care.