Magnetic oxides exhibit rich fundamental physics(1-4) and technologically desirable properties for spin-based memory, logic and signal transmission(5-7). Recently, spin-orbit-induced spin transport phenomena have been realized in insulating magnetic oxides by using proximate heavy metal layers such as platinum(8-10). In their metallic ferromagnet counterparts, such interfaces also give rise to a Dzyaloshinskii-Moriya interaction(11-13) that can stabilize homochiral domain walls and skyrmions with efficient current-driven dynamics. However, chiral magnetism in centrosymmetric oxides has not yet been observed. Here we discover chiral magnetism that allows for pure spin-current-driven domain wall motion in the most ubiquitous class of magnetic oxides, ferrimagnetic iron garnets. We show that epitaxial rare-earth iron garnet films with perpendicular magnetic anisotropy exhibit homochiral Neel domain walls that can be propelled faster than 800 m s(-1) by spin current from an adjacent platinum layer. We find that, despite the relatively small interfacial Dzyaloshinskii-Moriya interaction, very high velocities can be attained due to the antiferromagnetic spin dynamics associated with ferrimagnetic order.