Transitions among quantum Hall plateaux share a suite of remarkable experimental features, such as semicircle laws and duality relations, whose accuracy and robustness are difficult to explain directly in terms of the detailed dynamics of the microscopic electrons. They would naturally follow if the low-energy transport properties were governed by an emergent discrete duality group relating the different plateaux, but no explicit examples of interacting systems having such a group are known. Recent progress using the AdS/CFT correspondence has identified examples with similar duality groups, but without the dc ohmic conductivity characteristic of quantum Hall experiments. We use this to propose a simple holographic model for low-energy quantum Hall systems, with a nonzero dc conductivity that automatically exhibits all of the observed consequences of duality, including the existence of the plateaux and the semicircle transitions between them. The model can be regarded as a strongly coupled analogue of the old ‘composite boson’ picture of quantum Hall systems. Non-universal features of the model can be used to test whether it describes actual materials, and we comment on some of these in our proposed model. In particular, the model indicates the value 2/5 for low-temperature scaling exponents for transitions among quantum Hall plateaux, in agreement with the measured value 0.42±0.01.