AdS_5 x S^5 Black Hole Metric at O(alpha'^3)

We compute $O(\alpha'^3)$ corrections to the $AdS_5\times S^5$ black hole metric. We find that the radius of the $S^5$ depends on the radial $AdS_5$ coordinate. This completes the computation of Gubser, Klebanov and Tseytlin (hep-th/9805156). The fact that the metric no longer factorizes should modify the value of the Wilson line at finite temperature and the glueball mass spectrum.