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By freezing out the motion between particles in a high-energy storage ring, it should be possible to create threads of ions, offering research opportunities beyond the realm of standard accelerator physics. The usual heating due to intra-beam collisions should completely vanish, giving rise to a state of unprecedented brilliance. Despite a continuous improvement of beam cooling techniques, such as electron cooling and laser cooling, the ultimate goal of beam crystallization has not yet been reached in high-energy storage rings. Electron-cooled dilute beams of highly charged ions show liquid-like order with unique applications. An experiment using laser cooling suggested a reduction of intra-beam heating, although the results were ambiguous. Here we demonstrate the crystallization of laser-cooled Mg+ beams circulating in the radiofrequency quadrupole storage ring PALLAS at a velocity of 2,800 m s-1, which corresponds to a beam energy of 1 eV. A sudden collapse of the transverse beam size and the low longitudinal velocity spread clearly indicate the phase transition. The continuous ring-shaped crystalline beam shows exceptional stability, surviving for more than 3,000 revolutions without cooling.