We report on the energy- and momentum-resolved optical response of black phosphorus (BP) in its bulk form. Along the armchair direction of the puckered layers, we find a highly dispersive mode that is strongly suppressed in the perpendicular (zigzag) direction. This mode emerges out of the single-particle continuum for finite values of momentum and is therefore interpreted as an exciton. We argue that this exciton, which has already been predicted theoretically for phosphorene—the monolayer form of BP—can be detected by conventional optical spectroscopy in the two-dimensional case and might pave the way for optoelectronic applications of this emerging material.