We have studied here using high resolution resistance measurements the time and statistical behavior of abrupt resistance changes in a thin metal aluminum film undergoing electromigration. We reveal for the first time that early stage electromigration exhibits on-off intermittency. The intermittent resistance fluctuations are also shown to be scale invariant, an effect seen in the fluctuations of several physical systems including earthquakes, superconductor dynamics and stock markets. Finite size scaling of the resistance fluctuations demonstrates that they originate near a critical point.