Deposition of silver nanoparticles directly onto a Rhodamine Red monolayer covalently bound to glass is found to increase the photoluminescence by as much as 20 times depending on excitation wavelength and nanoparticle density. At the same time, the excited state lifetime is reduced by more than a factor of 2, the fluorescence spectrum is blue-shifted, and greater polarization anisotropy in the emission is observed. We attribute these effects to local enhancement of the optical fields near the molecules by interactions with silver plasmons. We approximately separate the relative contributions of increased absorption and increased emissive rate to the observed enhancement of fluorescence. A study of the spatial inhomogeneity of the effect using scanning confocal microscopy demonstrates that average enhancements at least twice as large are possible.