Elastic light-by-light scattering (γγ→γγ) is open to study at the Large Hadron Collider thanks to the large quasireal photon fluxes available in electromagnetic interactions of protons (p) and lead (Pb) ions. The γγ→γγ cross sections for diphoton masses m(γγ)>5 GeV amount to 12 fb, 26 pb, and 35 nb in p-p, p-Pb, and Pb-Pb collisions at nucleon-nucleon center-of-mass energies √(s(NN))=14, 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.