  The diffusivity of tagged particles is demonstrated to be very heterogeneous
on time scales comparable to or shorter than the $\alpha$ relaxation time
$\tau_{\alpha}$ ($\cong$ the stress relaxation time) in a highly supercooled
liquid via 3D molecular dynamics simulation. The particle motions in the
relatively active regions dominantly contribute to the mean square
displacement, giving rise to a diffusion constant systematically larger than
the Einstein-Stokes value. The van Hove self-correlation function $G_s(r,t)$ is
shown to have a long distance tail which can be scaled in terms of $r/t^{1/2}$
for $t \ls 3\tau_{\alpha}$. Its presence indicates heterogeneous diffusion in
the active regions. However, the diffusion process eventually becomes
homogeneous on time scales longer than the life time of the heterogeneity
structure ($\sim 3 \tau_{\alpha}$).
