  Motivated by the recent Coulomb drag experiment of M. P. Lilly et. al, we
study the Coulomb drag in a two-layer system with Landau level filling factor
$\nu=1/2$. We find that the drag conductivity in the incompressible paired
quantum Hall state at zero temperature can be finite. The drag conductivity is
also greatly enhanced above $T_c$, at which the transition between the weakly
coupled compressible liquids and the paired quantum Hall liquid takes place. We
discuss the implications of our results for the recent experiment.
