The production of two isolated photons at the Large Hadron Collider has applications in Higgs-boson phenomenology and in new-physics searches. In fact, measurements would provide more insight if a percent-level theoretical prediction were available. We account for next-to-next-to-next-to-leading order strong-interaction effects in the cross section for the first time. This is not only necessary to demonstrate the convergence of perturbation theory, but also results in a reduction of the theoretical uncertainty by a factor of three down to 3%. With this, we pave the way to improved analyses.