Experimental investigations of the Hall effect at the occurrence of autonomous current fluctuations in high-purity n-GaAs epitaxial layers at low temperatures show that the transition to chaos is accompanied by intermittent collapses in the Hall voltage. This may represent the significant third mechanism for a transition into chaos according to the Ruelle-Takens-Newhouse scenario. Basically, space charges accumulated in the filament boundaries yield different impact ionization probabilities at opposite sides of the filament destabilizing the current flow and causing multimodal oscillation phenomena originating at the filament borders.