In microorganisms, noise in gene expression gives rise to cell-to-cell variability in protein concentrations. In mammalian cells, protein levels also vary and individual cells differ widely in their responsiveness to uniform physiological stimuli. 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.