Cells in developing organisms must robustly assume the correct fate in order to fulfill their specific function. At the same time, cells are strongly affected by molecular fluctuations, i.e. 'noise', leading to inherent variability in individual cells. During development, some cells are thought to exploit such molecular noise to drive stochastic cell fate decisions, with cells randomly picking one cell fate out of several possible ones. Yet, how molecular noise drives such decisions is an open question. We address this question using a novel quantitative approach to study one of the best-understood stochastic cell fate decisions: the AC/VU decision in C. elegans gonad development. Here, two initially equivalent cells, Z1.ppp and Z4.aaa, interact, so that one cell becomes the anchor cell (AC) and the other a ventral uterine precursor cell (VU). It is thought that the symmetry is broken when small molecular fluctuations are amplified into cell fate by positive feedback loops in the Notch signaling pathway. To identify the noise sources that drive the AC/VU decision, we used a novel time-lapse microscopy approach to follow expression dynamics in live animals and single molecule FISH to quantify gene expression with single mRNA resolution. We found not only that random Z1.ppp/Z4.aaa birth order biased the decision outcome, with the first-born cell typically assuming VU fate, but that the strength of this bias and the speed of the decision decreased as the two cells were born closer together in time. Moreover, we find that the Notch ligand lag-2/Delta exhibited strongly stochastic expression already in the two mother cells, Z1.pp/Z4.aa. Combining experiments with mathematical models, we showed that the resulting asymmetry in lag-2/Delta levels inherited by the daughter cells, Z1.ppp/Z4.aaa, stochastic symmetry breaking when both cells are born at similar times. Together, our results suggest that two independent noise sources, birth order and stochastic lag-2/Delta expression, are exploited to amplify noise into cell fate in a manner that ensures a robust decision.