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Resolving momentum degrees of freedom of excitons, which are electron-hole pairs bound by the Coulomb attraction in a photoexcited semiconductor, has remained an elusive goal for decades. In atomically thin semiconductors, such a capability could probe the momentum-forbidden dark excitons, which critically affect proposed opto-electronic technologies but are not directly accessible using optical techniques. Here, we probed the momentum state of excitons in a tungsten diselenide monolayer by photoemitting their constituent electrons and resolving them in time, momentum, and energy. We obtained a direct visual of the momentum-forbidden dark excitons and studied their properties, including their near degeneracy with bright excitons and their formation pathways in the energy-momentum landscape. These dark excitons dominated the excited-state distribution, a surprising finding that highlights their importance in atomically thin semiconductors.