Self-propulsion plays a crucial role in biological processes and nanorobotics, enabling small systems to move autonomously in noisy environments. Here, we theoretically demonstrate that a bound skyrmion-skyrmion pair in a synthetic antiferromagnetic bilayer can function as a self-propelled topological object, reaching speeds of up to a hundred million body lengths per second-far exceeding those of any known synthetic or biological self-propelled particles. The propulsion mechanism is triggered by the excitation of back-and-forth relative motion of the skyrmions, which generates nonreciprocal gyrotropic forces, driving the skyrmion pair in a direction perpendicular to their bond. Remarkably, thermal noise induces spontaneous reorientations of the pair and momentary reversals of the propulsion, mimicking behaviors observed in motile bacteria and microalgae.