The theoretical framework developed by Rayleigh and Plateau in the 19th century has been remarkably accurate in describing macroscale experiments of liquid cylinder instability. Here we re-evaluate and revise the Rayleigh–Plateau instability for the nanoscale, where molecular dynamics experiments demonstrate its inadequacy. A new framework based on the stochastic lubrication equation is developed that captures nanoscale flow features and highlights the critical role of thermal fluctuations at small scales. Remarkably, the model indicates that classically stable (i.e. ‘fat’) liquid cylinders can be broken at the nanoscale, and this is confirmed by molecular dynamics.