We study the propagation of charm quarks, produced from the initial fu
sion of partons, in an equilibrating quark-gluon plasma which may be f
ormed in the wake of relativistic collisions of gold nuclei. Initial c
onditions are taken from a self-screened parton cascade model and the
chemical equilibration is assumed to proceed via gluon multiplication
and quark production. The energy loss suffered by the charm quarks is
obtained by evaluating the drag force generated by the scattering with
quarks and gluons in the medium. We find that the charm quarks may lo
se only about 10% of their initial energy in conditions likely to be a
ttained at the Relativistic Heavy Ion Collider, while they may lose up
to 40% of their energy while propagating in the plasma created at the
Large Hadron Collider. We discuss the implications for signals of the
quark-gluon plasma.