SOLID hydrogen is predicted1,2 to become metallic at high pressures. Although metallization was recently reported in high-pressure shock-wave compression experiments using liquid hydrogen3, efforts to understand the high-pressure behaviour of the solid phase have relied mainly on spectroscopic studies in the diamond-anvil cell4-6 and on ab initio calculations7-10. Central to these studies is the high-pressure crystal structure-something that is difficult to determine in the diamond-anvil cell-and its pressure dependence. Here we report X-ray diffraction measure-ments of the structure of single-crystal molecular hydrogen at pressures of up to 109 GPa for H2 and 119 GPa for D2. From these measurements we deduce the high-pressure equation of state (EOS: the volume-pressure relation). We find that solid hydro-gen is more compressible than previously thought, that the crystal becomes increasingly anisotropic with pressure, and that the difference in EOS between H2 and D2 is unexpectedly small. The 'softening' of the EOS relative to previous estimates4 increases by about 25% the expected transition pressure to the atomic phase. Our EOS differs significantly from that predicted by ab initio calculations7,9, indicating that theoretical understand-ing of the behaviour of dense hydrogen remains incomplete.