  A long-standing puzzle in density-functional theory is the issue of the
long-range behavior of the Kohn-Sham exchange-correlation potential at metal
surfaces. As an important step towards its solution, it is proved here, through
a rigurouos asymptotic analysis and accurate numerical solution of the
Optimized-Effective-Potential integral equation, that the Kohn-Sham exact
exchange potential decays as $\ln(z)/z$ far into the vacuum side of an {\it
extended} semi-infinite jellium. In contrast to the situation in {\it
localized} systems, like atoms, molecules, and slabs, this dominant
contribution does not arise from the so-called Slater potential. This
exact-exchange result provides a strong constraint on the suitability of
approximate correlation-energy functionals.
