Evidence for the light-by-light scattering process, , in ultraperipheral PbPb collisions at a centre-of-mass energy per nucleon pair of is reported. The analysis is conducted using a data sample corresponding to an integrated luminosity of recorded by the CMS experiment at the LHC. Light-by-light scattering processes are selected in events with two photons exclusively produced, each with transverse energy , pseudorapidity , diphoton invariant mass , diphoton transverse momentum , and diphoton acoplanarity below 0.01. After all selection criteria are applied, 14 events are observed, compared to expectations of events for the signal and for the background processes. The excess observed in data relative to the background-only expectation corresponds to a significance of 3.7 standard deviations, and has properties consistent with those expected for the light-by-light scattering signal. The measured fiducial light-by-light scattering cross section, , is consistent with the standard model prediction. The distribution is used to set new exclusion limits on the production of pseudoscalar axion-like particles, via the Image 1 process, in the mass range Image 2.