Elastic light-by-light scattering () is open to study at the Large Hadron Collider thanks to the large quasireal photon fluxes available in electromagnetic interactions of protons () and lead (Pb) ions. The cross sections for diphoton masses amount to 12 fb, 26 pb, and 35 nb in , , and Pb-Pb collisions at nucleon-nucleon center-of-mass energies , 8.8, and 5.5 TeV, respectively. Such a measurement has no substantial background in Pb-Pb collisions where one expects about 20 signal events per run, after typical detector acceptance and reconstruction efficiency selections.