Aircraft landing gear (100) provided with a bottom portion (110) that is steerable by means of a steering actuator (1) comprising a toothed wheel (70) that is secured to the steerable bottom portion (110) and that co-operates with a rack (20) that is movable in translation along an axial travel axis (X) and that has ends (21a, 21b) connected to pistons (30a, 30b) mounted to slide in respective cylinders (10a, 10b). Each connection between one of the pistons (30a, 30b) and the associated end of the rack (20) presents play (J) at least axially, and possibly also angular play (E), and at least one sealing gasket, referred to as an internal gasket (25), between the rack (20) and a piston (30a, 30b), the gasket being arranged to oppose movements of the rack (20) relative to the pistons (30a, 30b).