Bulk ZnO samples, epitaxially grown ZnO layers, and ZnO nanostructures frequently exhibit a characteristic emission band at $3.31\text{−}\mathrm{eV}$ photon energy whose origin is controversially discussed in the literature. Partly, this omnipresent band is ascribed to $(e,A^0)$ transitions of conduction band electrons to acceptors, which are abundant in relatively high concentrations but have not positively been identified. The band is, in particular, often reported after intentional $p$-type doping of ZnO, preferentially with group V species. In the present work, we study the $3.31\text{−}\mathrm{eV}$ band by low-temperature cathodoluminescence (CL) with high spatial resolution, by scanning electron microscopy, and by transmission electron microscopy (TEM). Line shape analyses at different temperatures give clear evidence that the band originates from an $(e,A^0)$ transition where the acceptor binding energy is $(130\pm 3)\mathrm{meV}$. The $3.31\text{−}\mathrm{eV}$ luminescence is exclusively emitted from distinct lines on sample surfaces and cross sections representing intersections with basal planes of the wurtzite hexagons. Correlating monochromatic CL images with TEM images, we conclude that the localized acceptor states causing the $3.31\text{−}\mathrm{eV}$ luminescence are located in basal plane stacking faults.