A tenet of special relativity is that no particle can exceed the speed of light. In certain magnetic materials, the maximum magnon group velocity serves as an analogous relativistic limit for the speed of magnetic solitons. Here, we drive domain walls to this limit in a low-dissipation magnetic insulator using pure spin currents from the spin Hall effect. We achieve record current-driven velocities in excess of 4300 meters per second-within similar to 10% of the relativistic limit-and we observe key signatures of relativistic motion associated with Lorentz contraction, which leads to velocity saturation. The experimental results are well explained through analytical and atomistic modeling. These observations provide critical insight into the fundamental limits of the dynamics of magnetic solitons and establish a readily accessible experimental framework to study relativistic solitonic physics.