  Spin Hall effect of spin-texture origin is explored theoretically for
antiferromagnetic (AF) metals. It is found that a vector chirality formed by
the N\'eel vector gives rise to a topological spin Hall effect. This is
topological since it is proportional to the winding number counted by in-plane
vector chirality along the sample edge, which can be nonvanishing for AF merons
but not for AF skyrmions. The effect is enhanced when the Fermi level lies near
the AF gap, and, surprisingly, at weak coupling with small AF gap. These
features are confirmed numerically based on the Landauer-B\"uttiker formula.
Important roles played by nonadiabatic processes and spin dephasing are pointed
out.
