We report the experimental discovery of autogenic cyclicity in delta foreset bedding that arises simply from steady water and sediment input under particular hydraulic characteristics. This autogenesis is intrinsic to Froude-supercritical flow associated with a train of upstream-migrating hydraulic jumps that delineate cyclic steps. Upstream migration of hydraulic jumps is associated with discrete packages of sediment accumulation on the foreset slope. This synchronism originates from the periodic alternation between supercritical and subcritical flow states on the delta topset just upstream of the shoreline, i.e., the topset foreset break of the delta. The alternation in turn depends on the distance from the topset foreset break to the nearest hydraulic jump immediately upstream. When the hydraulic jump is still in close proximity to the river mouth (delta shore), it reworks existing topset deposits (and perhaps upper foreset deposits as well) as it migrates upstream. Reworked sediment is then entrained into the subcritical flow between the shore and the hydraulic jump, which then emplaces this fine suspended sediment onto the foreset slope. As the hydraulic jump moves sufficiently far upstream of the mouth, the topset flow becomes supercritical, with a flow velocity sufficient to transport fine sediment offshore beyond the foreset. Under these conditions, the sediment emplaced on the foreset tends to be coarser material deposited via avalanching or proximal deposition from suspension. The details of this selective sedimentation vary according to the material in the topset bed near the mouth that is available for entrainment into the subcritical flow. Regardless of the details, however, distinct cyclic sedimentation of the delta foreset can be sustained as long as the inflow conditions of water and sediment dictate the formation of cyclic steps on the alluvial bed of the topset. Such hydraulic autogenesis accounts for a set of stratigraphic features that are common in ancient Gilbert deltas.