  We present the results of a large scale molecular dynamics computer
simulation study in which we investigate whether a supercooled Lennard-Jones
liquid exhibits dynamical heterogeneities. We evaluate the non-Gaussian
parameter for the self part of the van Hove correlation function and use it to
identify ``mobile'' particles. We find that these particles form clusters whose
size grows with decreasing temperature. We also find that the relaxation time
of the mobile particles is significantly shorter than that of the bulk, and
that this difference increases with decreasing temperature.
