The long-time self-diffusion of fluorescent molecular and colloidal tracers in a dense random packing of large (nondiffusing) spheres has been studied for the first time in situ, using fluorescense recovery after photobleaching. The long-time tracer diffusion coefficient depends uniquely on the ratio beta of the tracer size to the packing sphere size. This dependence is much stronger than that predicted by theories which neglect hydrodynamic interactions, emphasizing the importance of hydrodynamics on confined diffusion of finite-sized tracers. Hydrodynamic friction cah be described qualitatively by a mapping model of the pore space, which reproduces experimental diffusivities fairly well.