Grid cells provide a neural representation of space, by discharging when an animal traverses through the vertices of a periodic hexagonal grid spanning the environment. Although grid cells have been characterized in detail in rats, the fundamental question of what neural dynamics give rise to the grid structure remains unresolved. Two competing classes of models were proposed: network models, based on attractor dynamics, and oscillatory interference models, which propose that interference between somatic and dendritic theta-band oscillations (4-10 Hz) in single neurons transforms a temporal oscillation into a spatially periodic grid. So far, these models could not be dissociated experimentally, because rodent grid cells always co-exist with continuous theta oscillations. Here we used a novel animal model, the Egyptian fruit bat, to refute the proposed causal link between grids and theta oscillations. On the basis of our previous finding from bat hippocampus, of spatially tuned place cells in the absence of continuous theta oscillations, we hypothesized that grid cells in bat medial entorhinal cortex might also exist without theta oscillations. Indeed, we found grid cells in bat medial entorhinal cortex that shared remarkable similarities to rodent grid cells. Notably, the grids existed in the absence of continuous theta-band oscillations, and with almost no theta modulation of grid-cell spiking--both of which are essential prerequisites of the oscillatory interference models. Our results provide a direct demonstration of grid cells in a non-rodent species. Furthermore, they strongly argue against a major class of computational models of grid cells.