On nanotextured noble-metal surfaces, surface-enhanced Raman scattering (SERS) is observed, where Raman scattering is enhanced by a factor, G, that is frequently about one million, but underlying the factor G is a broad distribution of local enhancement factors, eta. We have measured this distribution for benzenethiolate molecules on a 330-nanometer silver-coated nanosphere lattice using incident light of wavelength 532 nanometers. A series of laser pulses with increasing electric fields burned away molecules at sites with progressively decreasing electromagnetic enhancement factors. The enhancement distribution P(eta)deta was found to be a power law proportional to (eta)(-1.75), with minimum and maximum values of 2.8 x 10(4) and 4.1 x 10(10), respectively. The hottest sites (eta >10(9)) account for just 63 in 1,000,000 of the total but contribute 24% to the overall SERS intensity.