The preferred retinal locus (PRL) is the position on the retina to which humans direct stimuli during fixation. In healthy normal eyes, it has been shown to be very stable across time and between different tasks. Previous measurements of the PRL have been made under monocular viewing conditions. The current study examines where the PRLs in the two eyes' retinas are when subjects fixate binocularly and whether they shift when the demand for the eyes to converge is changed. Our apparatus allows us to see exactly where binocular stimuli fell on the two retinas during binocular fixation. Thus, our technique bypasses some of the issues involved in measuring binocular alignment with subjective techniques and previous objective techniques that use conventional eye trackers. These results show that PRLs shift slightly but systematically as the demand for convergence increases. The shifts cause under-convergence (also called exo fixation disparity) for near targets. They are not large enough to cause a break in binocular fusion. The fixation disparity we observed with increasing vergence demand is similar to fixation disparity observed in previous reports.