Solid hydrogen, an electrical insulator, is predicted to become an alkali metal under extreme compression, although controversy surrounds the pressure required to achieve this. The electrical conductivity of hydrogen as a function of pressure and temperature is of both fundamental and practical interest-metallic hydrogen may be of relevance to planetary interiors, and has been suggested as a potential high-temperature superconductor. Calculations, suggest that depairing (destruction of the molecular bond) should occur around 340GPa, accompanied by the formation of an alkali metal at this pressure, or at substantially higher pressures,. Here we report that solid hydrogen does not become an alkali metal at pressures of up to 342 +/- 10GPa, achieved using a diamond anvil cell. This pressure (which is almost comparable to that at the centre of the Earth) significantly exceeds those reached in earlier experiments-216GPa (ref. 6) and 191GPa (ref. 7)-at which hydrogen was found to be non-metallic. The failure of solid hydrogen to become an alkali metal at the extreme pressures reported here has implications for our current theoretical understanding of the solid-state phase.