Little is known about controls on river avulsion at geological time scales longer than 104 years, primarily because it is difficult to link observed changes in alluvial architecture to well-defined allogenic mechanisms and to disentangle allogenic from autogenic processes. Recognition of Milankovitch-sale orbital forcing in alluvial stratigraphy would provide unprecedented age control in terrestrial deposits, and also exploit models of allogenic forcing enabling more rigorous testing of allocyclic and autocyclic controls. The Willwood Formation of the Bighorn Basin is a lower Eocene fluvial unit distinctive for its thick sequence of laterally extensive lithological cycles on a scale of 4 to 10 m. Intervals of red palaeosols that formed on overbank mudstones are related to periods of relative channel stability when gradients between channel belts and floodplains were low. The intervening drab, heterolithic intervals with weak palaeosol development are attributed to episodes of channel avulsion that occurred when channels became super-elevated above the floodplain. In the Deer Creek Amphitheater section in the McCullough Peaks area, these overbank and avulsion deposits alternate with a dominant cycle thickness of ca 7·1 m. Using integrated stratigraphic age constraints, this cyclicity has an estimated period of ca 21·6 kyr, which is in the range of the period of precession climate cycles in the early Eocene. Previous analyses of three older and younger sections in the Bighorn Basin showed a similar 7 to 8 m spacing of red palaeosol clusters with an estimated duration close to the precession period. Intervals of floodplain stability alternating with episodes of large-scale reorganization of the fluvial system could be entirely autogenic; however, the remarkable regularity and the match in time scales documented here indicate that these alternations were probably paced by allogenic, astronomically forced climate change.