We investigate a hybrid nanocomposite combining fluorescent dyes and ultrasmall (<3 nm) silver nanocrystals in a block copolymer micelle. Although the metal nanoparticles are significantly smaller than the electromagnetic skin depth, we observe a modification of the exciton lifetime and the nonradiative energy transfer among the dyes. This behavior is absent in a control experiment with dyes whose energetic levels are far from the plasmonic resonance, establishing the plasmonic nature of the interaction.