Lead halide perovskites have emerged as promising new semiconductor materials for high-efficiency photovoltaics, light-emitting applications and quantum optical technologies. Their luminescence properties are governed by the formation and radiative recombination of bound electron-hole pairs known as excitons, whose bright or dark character of the ground state remains unknown and debated. While symmetry analysis predicts a singlet non-emissive ground exciton topped with a bright exciton triplet, it has been predicted that the Rashba effect may reverse the bright and dark level ordering. Here, we provide the direct spectroscopic signature of the dark exciton emission in the low-temperature photoluminescence of single formamidinium lead bromide perovskite nanocrystals under magnetic fields. The dark singlet is located several millielectronvolts below the bright triplet, in fair agreement with an estimation of the long-range electron-hole exchange interaction. Nevertheless, these perovskites display an intense luminescence because of an extremely reduced bright-to-dark phonon-assisted relaxation.