What does a black hole look like? The first images of the supermassive black hole M87* display a bright ring encircling the event horizon, which appears as a dark patch in its surrounding emission. But Einstein's theory of general relativity predicts that within this image there also lies a thin "photon ring" consisting of multiple mirror images of the main emission. These images arise from photons that orbited around the black hole multiple times, probing the warped space-time geometry just outside its horizon. The photon ring carries an imprint of the strong gravity in this region and encodes fundamental properties of the black hole (including, for instance, its quasinormal mode spectrum). A measurement of this predicted (but not yet observed) ring could provide a precise test of general relativity and will be the target of a NASA mission proposed to fly within the next decade.