  The spin Hall effect (SHE), which converts a charge current into a transverse
spin current, has long been believed to be a phenomenon induced by the
spin--orbit coupling. Here, we propose an alternative mechanism to realize the
intrinsic SHE through a chiral magnetic structure that breaks the spin rotation
symmetry. No spin--orbit coupling is needed even when the scalar spin chirality
vanishes, different from the case of the topological Hall effect. In known
chiral antiferromagnetic compounds Mn$_3X$ ($X=$ Ga, Ge, and Sn), for example,
we indeed obtain large spin Hall conductivities based on \textit{ab initio}
calculations. Apart further developing the conceptual understanding of the SHE,
our work suggests an alternative strategy to design spin Hall materials without
involving heavy elements, which may be advantageous for technological
applications.
