We present a first-principles molecular dynamics study of water near and above the critical point (T = 647 K, p = 0.32 g/cm(3)). We find that the systems undergo fast dynamics with continuous formation and breaking of H bonds. At low density, the system fragments mostly into trimers, dimers, and single molecules. At a higher density, more complex structures appear and an extended, albeit very dynamical, H-bond network can be identified. These structures have important consequences for the screening properties of the system. This offers a clue to understanding the peculiar chemical behavior of a supercritical system and allows thermodynamical tuning of its solvent properties.