Understanding the physics of gas giants requires knowledge about the behavior of hydrogen at extreme pressures and temperatures. Molecular hydrogen in these planets is supercritical, and has been considered as a physically homogeneous state where no differences can be made between a liquid and a gas and where all properties undergo no marked or distinct changes with pressure and temperature, the picture believed to hold below the dissociation and metallization transition. Here, we show that in Jupiter and Saturn, supercritical molecular hydrogen undergoes a dynamic transition around 10 GPa and 3000 K from the "rigid" liquid state to the "nonrigid" gas-like fluid state at the Frenkel line recently proposed, with the accompanying qualitative changes of all major physical properties. The consequences of this finding are discussed, including a physically justified way to demarcate the interior and the atmosphere in gas giants.