Prior to COVID-19, EU-level activity in health appeared limited. While the pandemic raised the EU’s health profile, it also questioned future development: crisis response, or a fundamental change in EU Member State health competence? This chapter examines whether COVID-19 can be said to accelerate EU-level activity in health by reference to implementing a European Health Union (EHU) and proposals for Treaty change between May 2020 and September 2021. Kingdon’s Multiple Streams Framework and “windows of opportunity” model is used to explore the chances for success for the EHU proposals. This frames confluence of the problem stream (COVID-19 crisis response and wider concerns about EU–national competence interaction), the politics stream (the European Commission and national politicians), and the policy stream (Commission proposals, the EHU initiative manifesto, and the Conference on the Future of Europe). This exploration helps shape understanding of how EU health policy evolves, and more specifically whether COVID-19 accelerated change.