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We report the observation of an extremely large magnetoresistance (up to 15 000 000% at 1.8 K in a magnetic field of 9 T) in a simple chemical element, gray arsenic, in which the magnitude of the magnetoresistance increases as approximately the square of the magnetic field strength without any signs of saturation. The Hall-effect study confirms that gray arsenic is a nearly perfect ``compensated semimetal,'' with a small concentration of very mobile carriers, which lead to an extremely large magnetoresistance. The analysis of Shubnikov--de Haas oscillations reveals a nontrivial \ensuremath{\pi} Berry phase, a strong signature of Dirac fermions with three-dimensional dispersion. Furthermore, in the presence of parallel magnetic and electric fields, a weak antilocalization effect and a pronounced negative longitudinal magnetoresistance, which may be linked to novel topological states, are also observed. These findings which uncover the material's basis in gray arsenic not only open avenues in spintronics and magnetic sensor applications but also provide more platforms to study topological materials.