The unusual properties of two-dimensional electron systems that give rise to the quantum Hall effect have prompted the development of new microscopic models for electrical conduction [1-6]. The bulk properties of the quantum Hall effect have also been studied experimentally using a variety of probes including transport [7,8], photoluminescence [9,10], magnetization  and capacitance [12,13] measurements. However, the fact that two-dimensional electron systems typically exist some distance (about 1,000 Angstrom) beneath the surface of the most semiconductor has presented an important obstacle to more direct measurements of microscopic electronic structure in the quantum Hall regime. Here we introduce a cryogenic scanning-probe technique-'subsurface charge accumulation' imaging-that permits very high resolution examination of systems of mobile electrons inside materials. We use this technique to image directly the nanometre-scale electronic structures that exist in the quantum Hall regime.