A model is developed by which path integration as observed in many animal species could be implemented neurobiologically. The proposed architecture is able to describe the navigation behaviour of Cataglyphis ants, and that of other social insects, at the level of interacting neurons. The basic idea of this architecture is the concept of activity patterns travelling along neural chains. Although experimental evidence has yet to be provided, this concept seems biologically plausible and not limited to the navigation problem. Neural chains are able to represent variables by activity patterns with high accuracy and temporal stability. Moreover, they are able to integrate incremental signals with high precision. Cyclical chains of neurons show superior performance as soon as cyclical variables are to be represented and integrated. Finally, representation of cyclical variables by travelling activity peaks allows simple approximations of goniometric functions as they are used in path integration systems.