  One of the challenges in relating experimental measurements of the
suppression in the number of J/\psi mesons produced in heavy ion collisions to
lattice QCD calculations is that whereas the lattice calculations treat J/\psi
mesons at rest, in a heavy ion collision a c\bar c pair can have a significant
velocity with respect to the hot fluid produced in the collision. The putative
J/\psi finds itself in a hot wind. We present the first rigorous
non-perturbative calculation of the consequences of a wind velocity v on the
screening length L_s for a heavy quark-antiquark pair in hot N=4 supersymmetric
QCD. We find L_s(v,T) = f(v)[1-v^2]^{1/4}/\pi T with f(v) only mildly dependent
on v and the wind direction. This L_s(v,T)\sim L_s(0,T)/\sqrt{\gamma} velocity
scaling, if realized in QCD, provides a significant additional source of J/\Psi
suppression at transverse momenta which are high but within experimental reach.
