The radiative and nonradiative decay rates of lissamine dye molecules, chemically attached to differently sized gold nanoparticles, are investigated by means of time-resolved fluorescence experiments. A pronounced fluorescence quenching is observed already for the smallest nanoparticles of 1 nm radius. The quenching is caused not only by an increased nonradiative rate but, equally important, by a drastic decrease in the dye's radiative rate. Assuming resonant energy transfer to be responsible for the nonradiative decay channel, we compare our experimental findings with theoretical results derived from the Gersten-Nitzan model.