Evidence for light-by-light (LbL) scattering, gamma gamma -> gamma gamma, in ultraperipheral PbPb collisions at a nucleon-nucleon center of-mass energy of 5.02 TeV is reported. LbL scattering processes are selected in events with just two photons produced, with transverse energy E-T(gamma) > 2 GeV, pseudorapidity vertical bar eta(gamma)vertical bar < 2.4; and diphoton invariant mass m(gamma gamma) > 5 GeV, transverse momentum p(T)(gamma gamma) < 1 GeV, and acoplanarity (1 - Delta phi(gamma gamma)/pi) < 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 4.10 sigma. The measured fiducial LbL scattering cross section, sigma(fid)(gamma gamma -> gamma gamma) = 122 +/- 46 (stat) +/- 29 (syst) +/- 4 (theo) nb is consistent with the standard model prediction.