Noisy gene expression or unequal partition of molecules during cell division are increasingly recognized as key sources of non-genetic cell-to-cell heterogeneity but the consequences for disease progression and drug efficiency are little understood. Through single-cell imaging, Spencer et al. now show that pre-existing cell-to-cell differences in the levels of signalling proteins determine whether the addition of an external death signal will kill a cell by apoptosis or not — and how quickly it happens. The mechanism may explain the phenomenon of 'fractional killing', in which repeated rounds of chemotherapy kill some but not all cells in a tumour. From an evolutionary perspective, such systems-level phenotypic variation — not based on genetic or epigenetic modifications — offers wider adaptive potential to populations of living organisms. Noise in gene expression gives rise to cell-to-cell variability in protein concentrations and is increasingly recognized as a key source of non-genetic differences between cells. Through single cell imaging, it has now been possible to demonstrate that pre-existing differences in the levels of signalling proteins determine whether the addition of an external death signal will kill a cell or not—and how fast. This has implications for understanding 'fractional killing' of tumour cells after chemotherapy, in which some but not all tumour cells die. In microorganisms, noise in gene expression gives rise to cell-to-cell variability in protein concentrations1,2,3,4,5,6,7. In mammalian cells, protein levels also vary8,9,10 and individual cells differ widely in their responsiveness to uniform physiological stimuli11,12,13,14,15. In the case of apoptosis mediated by TRAIL (tumour necrosis factor (TNF)-related apoptosis-inducing ligand) it is common for some cells in a clonal population to die while others survive—a striking divergence in cell fate. Among cells that die, the time between TRAIL exposure and caspase activation is highly variable. Here we image sister cells expressing reporters of caspase activation and mitochondrial outer membrane permeabilization after exposure to TRAIL. We show that naturally occurring differences in the levels or states of proteins regulating receptor-mediated apoptosis are the primary causes of cell-to-cell variability in the timing and probability of death in human cell lines. Protein state is transmitted from mother to daughter, giving rise to transient heritability in fate, but protein synthesis promotes rapid divergence so that sister cells soon become no more similar to each other than pairs of cells chosen at random. Our results have implications for understanding ‘fractional killing’ of tumour cells after exposure to chemotherapy, and for variability in mammalian signal transduction in general.