Throughout much of condensed matter science, correlated disorder is a key to material function. While structural and compositional defects are known to exist within a variety of metal-organic frameworks (MOFs), the prevailing understanding is that these defects are only ever included in a random manner. Here we show--using a combination of diffuse scattering, electron microscopy, anomalous X-ray scattering and pair distribution function measurements--that correlations between defects can in fact be introduced and controlled within a hafnium terephthalate MOF. The nanoscale defect structures that emerge are an analogue of correlated Schottky vacancies in rocksalt-structured transition metal monoxides and have implications for storage, transport, optical and mechanical responses. Our results suggest how the diffraction behaviour of some MOFs might be reinterpreted, and establish a strategy of exploiting correlated nanoscale disorder as a targetable and desirable motif in MOF design.