Place-modulated activity among neurons in the hippocampal formation presents a means to organize contextual information in the service of memory formation and recall. One particular spatial representation, that of grid cells, has been observed in the entorhinal cortex (EC) of rats and bats, but has yet to be described in single units in primates. Here we examined spatial representations in the EC of head-fixed monkeys performing a free-viewing visual memory task. Individual neurons were identified in the primate EC that emitted action potentials when the monkey fixated multiple discrete locations in the visual field in each of many sequentially presented complex images. These firing fields possessed spatial periodicity similar to a triangular tiling with a corresponding well-defined hexagonal structure in the spatial autocorrelation. Further, these neurons showed theta-band oscillatory activity and changing spatial scale as a function of distance from the rhinal sulcus, which is consistent with previous findings in rodents. These spatial representations may provide a framework to anchor the encoding of stimulus content in a complex visual scene. Together, our results provide a direct demonstration of grid cells in the primate and suggest that EC neurons encode space during visual exploration, even without locomotion.