While the British electorate was asked to vote on a simple-sounding question during the UK referendum on EU membership in June 2016, the issues at play were extremely complex. In order to help potential voters make sense of the debate, the authors ran a free Massive Open Online Course (MOOC) on the referendum in the weeks leading up to the vote. The core of the MOOC featured all the common characteristics of this type of course: weekly video lectures, quizzes, question and answer sessions, forums and personal journals which participants could use to share and reflect. To date, little research has been done on the potential for this course format to improve the public's understanding of, and engagement with, EU-related politics and policy issues. Consequently, this paper proposes some initial reflections on the opportunities and challenges presented by this MOOC for fostering broad public engagement with politics in the EU. By considering issues of format, attendance and attrition, participation and power dynamics, we identify the challenges for harnessing MOOCs as a pedagogical and communicative tool for counteracting the EU knowledge deficit