The development and maintenance of an epithelium requires finely balanced rates of growth and cell death. However, the mechanical and biochemical mechanisms that ensure proper feedback control of tissue growth(1-4), which when deregulated contribute to tumorigenesis, are poorly understood. Here we use the fly notum as a model system(5) to identify a novel process of crowding-induced cell delamination that balances growth to ensure the development of well-ordered cell packing. In crowded regions of the tissue, a proportion of cells undergo a serial loss of cell-cell junctions and a progressive loss of apical area, before being squeezed out by their neighbours. This path of delamination is recapitulated by a simple computational model of epithelial mechanics, in which stochastic cell loss relieves overcrowding as the system tends towards equilibrium. We show that this process of delamination is mechanistically distinct from apoptosis-mediated cell extrusion(6-8) and precedes the first signs of cell death. Overall, this analysis reveals a simple mechanism that buffers epithelia against variations in growth. Because live-cell delamination constitutes a mechanistic link between epithelial hyperplasia and cell invasion, this is likely to have important implications for our understanding of the early stages of cancer development.