Cold calling effectively incentivizes all students to actively prepare contributions to a class discussion, but some find it terrifying. Rewarding voluntarily speaking in class is less off-putting, and can be valuable for students who participate; however, it can allow a large fraction of the class to disengage. Agora is an open-source app designed to serve as a middle ground between these extremes, with the added benefit that it automatically produces an assessment of each student’s engagement. The key ideas are to give students control over whether their hand is raised or lowered, to choose randomly among students with raised hands, and to give participation credit to all students who were considered every time a speaker is chosen. The system has various other features to facilitate deployment in large classes including multiple queues to support concurrent questions on different topics; a message board to allow students to communicate discretely with the instructor; and polling. We deployed the system in three offerings of a large undergraduate class and demonstrate its effectiveness in terms of learning outcomes, gender balance in participation, and student satisfaction.