For decades, two-dimensional electron gases (2DEG) have allowed important experimental discoveries(1,2) and conceptual developments in condensed-matter physics(3). When combined with the unique electronic properties of two-dimensional crystals, they allow rich physical phenomena to be probed at the quantum level(4,5). Here, we create a 2DEG in black phosphorus-a recently added member of the two-dimensional atomic crystal family(6-8)-using a gate electric field. The black phosphorus film hosting the 2DEG is placed on a hexagonal boron nitride substrate. The resulting high carrier mobility in the 2DEG allows the observation of quantum oscillations. The temperature and magnetic field dependence of these oscillations yields crucial information about the system, such as cyclotron mass and lifetime of its charge carriers. Our results, coupled with the fact that black phosphorus possesses anisotropic energy bands with a tunable, direct bandgap(6-15), distinguish black phosphorus 2DEG as a system with unique electronic and optoelectronic properties.