Utilizing first-principles quantum transport calculations, we investigate the role of local fields in conductor surface electromigration. A nanometer thick Ag(100) thin film is adopted as our prototypical conductor, where we demonstrate the existence of intense local electric fields at atomic surface defects under an external bias. It is shown that such local fields can play an important role in driving surface electromigration and electrical breakdown. The intense fields originate from the relatively short (atomic-scale) screening lengths common to most elemental metals. This general short-range screening trend is established self-consistently within an intuitive picture of linear response electrostatics. The findings shed new light on the underlying physical origins of surface electromigration and point to the possibility of harnessing local fields to engineer electromigration at the nanoscale.