Evidence for light-by-light (LbL) scattering, γγ → γγ, in ultraperipheral PbPb collisions at a nucleon-nucleon centerof- mass energy of 5.02 TeV is reported. LbL scattering processes are selected in events with just two photons produced, with transverse energy Eγ T > 2 GeV, pseudorapidity |ηγ| < 2.4; and diphoton invariant mass mγγ > 5 GeV, transverse momentum pγγ T < 1 GeV, and acoplanarity (1 − Δφγγ/π) < 0.01. After all selection criteria, 14 events are observed, compared to 11.1 ± 1.1 (theo) and 3.8 ± 1.3 (stat) events expected for signal and background processes respectively. The significance of the signal excess over the background-only hypothesis is 4.1σ. The measured fiducial LbL scattering cross section, σfid(γγ → γγ) = 122 ± 46 (stat) ±29 (syst) ±4 (theo) nb is consistent with the standard model prediction.