  We calculate for the first time the complex potential between a heavy quark
and antiquark at finite temperature across the deconfinement transition in
lattice QCD. The real and imaginary part of the potential at each separation
distance $r$ is obtained from the spectral function of the thermal Wilson loop.
We confirm the existence of an imaginary part above the critical temperature
$T_C$, which grows as a function of $r$ and underscores the importance of
collisions with the gluonic environment for the melting of heavy quarkonia in
the quark-gluon-plasma.
