Elastic light-by-light scattering (γ γ → γ γ) is open to study at the Large Hadron Collider thanks to the large quasi-real photon fluxes available in electromagnetic interactions of protons (p) and lead (Pb) ions. The γ γ → γ γ cross sections for diphoton masses mγγ > 5 GeV amount to 105 fb, 260 pb, and 370 nb in p-p, p-Pb, and Pb-Pb collisions at nucleon-nucleon center-of-mass energies √ s NN = 14TeV, 8.8 TeV, and 5.5 TeV respectively. Such a measurement has no substantial backgrounds in Pb-Pb collisions where one expects about 70 signal events per run, after typical detector acceptance and reconstruction efficiency selections.