Solid hydrogen, a simple system consisting only of protons and electrons, exhibits a variety of structural phase transitions at high pressures. Experimental studies＇ based on static compression up to about 230 GPa revealed three relevant phases of solid molecular hydrogen: phase I (high-temperature, low-pressure phase), phase II (low-temperature phase) and phase III (high-pressure phase). Spectroscopic data suggest that symmetry breaking; possibly related to orientational ordering(1,2), accompanies the transition into phases II and III. The boundaries dividing the three phases exhibit a strong isotope effect(3), indicating that the quantum-mechanical properties of hydrogen nuclei are important. Here we report the quantum distributions of protons in the three phases of solid hydrogen, obtained by a first-principles path-integral molecular dynamics method. We show that quantum fluctuations of protons effectively hinder molecular rotation-that is, a quantum localization occurs. The obtained crystal structures have entirely different symmetries from those predicted by the conventional simulations which treat protons classically.