Investigating closely stacked GaN/AlN multiple quantum wells (MQWs) by means of cathodoluminescence spectroscopy directly performed in a scanning transmission electron microscope, we have reached an ultimate spatial resolution of σCL=1.8nm. The pseudomorphically grown MQWs with high interface quality emit in the deep ultraviolet spectral range. Demonstrating the capability of resolving the 10.8 nm separated, ultra-thin quantum wells, a cathodoluminescence profile was taken across individual ones. Applying a diffusion model of excitons generated by a Gaussian-broadened electron probe, the spatial resolution of cathodoluminescence down to the free exciton Bohr radius scale has been determined.