Grid cells are believed to play a central role in determining an animal’s sense of its location in space. A single grid cell fires only when the animal is located in particular positions in its environment. Grid cells are functionally organized in sets, called modules. Here we address the stability of the grid cell code for the animal’s position. In the absence of sensory cues that inform the animal about its position, e.g., in the dark, the state of each module might be perturbed by noise. If each module accumulates noise independently, this would cause catastrophic readout errors. Consequently, the grid cells would no longer represent any valid position. We argue that the different modules should be coupled, in order to obtain a stable representation of a continuous position over time. We propose a theory of coupled grid cell modules, where the coupling is implemented by a plausible neural circuit. This coupling allows the system to represent positions coherently even under the influence of noise, without compromising its ability to represent a large range of positions.