Studies of high-acuity visual processing in awake animals are invariably faced with the difficulty of accounting for the effects of eye movements on the retinal stimulus. Animals that are well-trained to maintain precise fixation continuously make involuntary eye movements, composed of both microsaccades and drift. Even in anaesthetized and paralysed animals, the eyes undergo slow drifts, as well as movements tied to heartbeat and respiration. The resulting uncertainty in the retinal stimulus can be large relative to the fine receptive fields (RFs) of neurons in primary visual cortex (V1), which are fixed in retinotopic coordinates. Conventional eye-tracking methods, such as implanted scleral eye coils and optical tracking techniques, have accuracies comparable to the magnitude of the fixational eye movements themselves (about 0.1 degrees), making them ill-suited to correct for such fine-grained changes in eye position. Thus, without accurately accounting for eye movements, the stimulus presented to such neurons is both uncontrolled and unknown, greatly limiting analyses of neural stimulus processing, cortical variability and the role of eye movements in visual processing. This is especially true for V1 neurons representing the central portion of the visual field (the fovea), which have extremely small RFs. As a result, relatively little is known about whether they process visual stimuli differently from neurons representing the non-foveal visual field, which is an important question given the overrepresentation of the fovea throughout visual cortex10 and the critical role the fovea has in a variety of high-acuity visual behaviors. Although basic tuning properties of foveal V1 neurons have been measured the detailed functional descriptions of V1 stimulus processing that have been developed for parafoveal neurons have yet to be tested, and important questions about functional specialization in the fovea remain. To address these problems, here we present a method for inferring an animals eye position using the activity of the V1 neurons themselves, leveraging their finely tuned RFs to derive precise information about the position of the stimulus on the retina. Our method utilizes multielectrode recordings and a recently developed nonlinear modelling approach to estimate an animals eye position, along with its associated uncertainty, with the high spatial and temporal resolutions needed to study foveal V1 neurons. We demonstrate this approach using multielectrode array recordings from awake behaving macaques, and show that it allows for estimation of eye position with an accuracy on the order of 1 min of arc. Our method yields eye-tracking improvements in both foveal and parafoveal recordings, and is robust to the number and composition of the recorded units. Using this method allows us to obtain detailed functional models of the stimulus processing of foveal V1 neurons that are otherwise largely or entirely obscured by eye movements. In addition to allowing detailed analyses of high-resolution stimulus processing, our method can identify and correct for the effects of eye movements on measures of cortical variability, which has important implications for studies of neural coding more generally.