The crystal structure and equation of state of solid hydrogen have been determined directly to 26.5 gigapascals at room temperature by new synchrotron x-ray diffraction techniques. Solid hydrogen remains in the hexagonal close-packed structure under these pressure-temperature conditions and exhibits increasing structural anisotropy with pressure. The pressure-volume curve determined from the x-ray data represents the most accurate experimental measurement of the equation of state to date in this pressure range. The results remove the discrepancy between earlier indirect determinations and provide a new experimental constraint on the molecular-to-atomic transition predicted at higher pressures.