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We describe an apparatus to measure the diffusion of dilute fluorophores in molecularly thin liquid films within a surface forces apparatus (SFA). The design is a significant modification of the traditional SFA in that it allows one to combine nanorheology with the single-molecule sensitive technique of fluorescence correlation spectroscopy. The primary enabling idea was to place a miniaturized SFA onto the stage of an optical microscope equipped with a long working distance objective and illuminated by a femtosecond laser. A secondary enabling idea was that the silver coating on the backside of mica, normally used in the traditional SFA design for interferometric measurements of the film thickness, was replaced by multilayer dielectric coatings that allowed simultaneous interferometry and fluorescence measurements in different regions of the optical spectrum. To illustrate the utility of this instrument, we contrast the translational diffusion of rhodamine dye molecules (in the solvent, 1,2-propane diol), in the unconfined bulk state and confined between mica sheets to the thickness 2.5 nm. The diffusion coefficient is found to decrease by 2 orders of magnitude under confinement.