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Motivated by the recent Coulomb drag experiment of M. P. Lilly et. al, westudy 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 pairedquantum Hall state at zero temperature can be finite. The drag conductivity isalso greatly enhanced above $T_c$, at which the transition between the weaklycoupled compressible liquids and the paired quantum Hall liquid takes place. Wediscuss the implications of our results for the recent experiment.Comment: 4 pages, 1 figure included, replaced by the published versio

Coulomb drag as a signature of the paired quantum Hall state