By combining density functional molecular dynamics simulations with a thermodynamic integration technique, we determine the free energy of metallic hydrogen and silica, SiO2, at megabar pressures and thousands of degrees Kelvin. Our ab initio solubility calculations show that silica dissolves into fluid hydrogen above 5000 K for pressures from 10 and 40 Mbars, which has implications for the evolution of rocky cores in giant gas planets like Jupiter, Saturn, and a substantial fraction of known extrasolar planets. Our findings underline the necessity of considering the erosion and redistribution of core materials in giant planet evolution models, but they also demonstrate that hot metallic hydrogen is a good solvent at megabar pressures, which has implications for high-pressure experiments.