  We propose a quantitative measure of a time scale on which Fickian diffusion
sets in for supercooled liquids and use Brownian Dynamics computer simulations
to determine the temperature dependence of this onset time in a Lennard-Jones
binary mixture. The time for the onset of Fickian diffusion ranges between 6.5
and 31 times the $\alpha$ relaxation time (the $\alpha$ relaxation time is the
characteristic relaxation time of the incoherent intermediate scattering
function). The onset time increases faster with decreasing temperature than the
$\alpha$ relaxation time. Mean squared displacement at the onset time increases
with decreasing temperature.
