Scanning tunnelling microscopy and atomic force microscopy can be used to study the electronic and structural properties of surfaces, as well as molecules and nanostructures adsorbed on surfaces, with atomic precision(1-7), but they cannot directly probe the distribution of charge in these systems. However, another form of scanning probe microscopy, Kelvin probe force microscopy, can be used to measure the local contact potential difference between the scanning probe tip and the surface, a quantity that is closely related to the charge distribution on the surface(8-12). Here, we use a combination of scanning tunnelling microscopy, atomic force microscopy and Kelvin probe force microscopy to examine naphthalocyanine molecules (which have been used as molecular switches(13)) on a thin insulating layer of NaCl on Cu(111). We show that Kelvin probe force microscopy can map the local contact potential difference of this system with submolecular resolution, and we use density functional theory calculations to verify that these maps reflect the intramolecular distribution of charge. This approach could help to provide fundamental insights into single-molecule switching and bond formation, processes that are usually accompanied by the redistribution of charge within or between molecules(14-16).