The invention relates to an aircraft undercarriage having a leg (2) pivotally mounted on a structure of the aircraft to pivot about a pivot axis (X1) between a deployed position and a retracted position, the undercarriage including a foldable brace (3a, 3b) comprising two hinged-together elements, one of which is hinged to the leg and the other of which is hinged to the structure of the aircraft,in such a manner that when the leg is in the deployed position, the two brace elements are locked together in a substantially aligned position, the undercarriage also being provided with a rotary drive actuator (10) having an outlet shaft acting on one of the elements of the foldable brace in order to cause the leg to pivot between its two positions. The drive actuator is pivotally mounted on thestructure of the aircraft to pivot about an axis of rotation (X3) of the outlet shaft, the drive actuator having a casing (12) connected by a reaction rod (13) to the leg in order to take up the torque developed by the drive actuator when driving the undercarriage.