The unique optical properties of noble metal nanoparticles have been used to design a label-free biosensor in a chip format. In this paper, we demonstrate that the size of gold nanoparticles significantly affects the sensitivity of the biosensor. Gold nanoparticles with diameters in the range of 12-48 nm were synthesized in solution and sensor chips were fabricated by chemisorption of these nanoparticles on amine-functionalized glass. Sensors fabricated from 39-nm-diameter gold nanoparticles exhibited maximum sensitivity to the change of the bulk refractive index and the largest "analytical volume", defined as the region around the nanoparticle within which a change in refractive index causes a change in the optical properties of the immobilized nanoparticles. The detection limit for streptavidin-biotin binding of a sensor fabricated from 39-nm-diameter nanoparticles was 20-fold better than a previously reported sensor fabricated from 13-nm-diameter gold nanoparticles. We also discuss several other factors that could improve the performance of the next generation of these immobilized metal nanoparticle sensors.