Amyloid fibrils, which are polymeric assemblies of protein molecules, have been intensively studied on a structural level, yet due to complications such as the disorder within the molecules, several aspects of their structure remain mysterious. Similarly, the kinetics of assembly are not well understood. Here we investigate the electric dipole moment of beta-lactoglobulin fibrils, a model amyloid fibril system, by applying the technique of transient electric birefringence. This moment appears to be large, and comparable to the total moment of the constituent protein monomers if they were joined in a chain, head-to-tail, without changing conformation, suggesting an ordered joining of monomers in the fibril. Such an ordered assembly may have implications for the assembly mechanism of beta-lactoglobulin fibrils in particular, and amyloid fibrils in general.