The phase diagram of high-pressure hydrogen is of great interest for fundamental research, planetary physics, and energy applications. A first-order phase transition in the fluid phase between a molecular insulating fluid and a monoatomic metallic fluid has been predicted. The existence and precise location of the transition line is relevant for planetary models. Recent experiments reported contrasting results about the location of the transition. Theoretical results based on density functional theory are also very scattered. We report highly accurate coupled electron-ion Monte Carlo calculations of this transition, finding results that lie between the two experimental predictions, close to that measured in diamond anvil cell experiments but at 25-30 GPa higher pressure. The transition along an isotherm is signaled by a discontinuity in the specific volume, a sudden dissociation of the molecules, a jump in electrical conductivity, and loss of electron localization.high pressure | phase transitions | quantum Monte Carlo | hydrogen metallization | molecular dissociation H ydrogen is the simplest element of the periodic table and a paradigmatic element in developing general physical theories of condensed matter. Despite the simple electronic structure, its phase diagram is unexpectedly rich, ranging from the normal three-phase equilibria (solid-liquid-gas) of the lowpressure molecular system to the fully dissociated and ionized plasma states at extreme conditions of temperature and pressure. Accurate knowledge of its phase diagram is highly relevant as testified by the continuing intense research activity over the last half century (1-5). Its relevance in nature arises because it is the most abundant element in the universe and, together with the next simplest element helium, constitutes 70-90% of the atmosphere of the giant planets, Jupiter and Saturn, and of the many, recently discovered, exoplanets. Also, it is the putative element for nuclear fusion for energy applications.The longest outstanding issue concerns the metal-insulator transition and its interplay with molecular dissociation. Molecular dissociation can occur either upon increasing temperature in the low-pressure fluid or upon increasing pressure in the low-temperature crystalline phase, or even as a combined action of temperature and pressure in the denser molecular fluid (5). The first prediction of metallization at zero temperature suggested that the molecular crystal would become atomic and transform to a simple metal above 25 GPa (1). Later experiments with higher pressures up to at least 360 GPa have found no convincing evidence of the metallic state at least below room temperature. However, they have revealed a rich phase diagram with a sequence of phase transformations in the molecular solid and the possibility of a semimetallic state (3, 6-13).The metallic state has been unequivocally observed in the dense fluid in the range of 100-200 GPa and estimated temperatures of 2,000-3,000 K by dynamical compression experiments (5, 14-16). Using the ...