1. Procellariiform birds accumulate large fat reserves during the nestling period; much of this is metabolized prior to fledging. We suggest that these energy reserves result from chronic overfeeding, which provides insurance against stochastic variation in food provisioning. 2. We develop a simulation model based on food provisioning and physiological measurements of Leach's storm-petrels and assess fat accumulation as a function of meal size. The simulations reveal that a level of food provisioning sufficient for accumulating, on average, the fat reserves of a typical fledgling results in the starvation of many chicks because of the chance occurrence of long periods of below-average feeding. Fledging success can be elevated by increasing meal size, but this results in overfeeding on average and the accumulation of unnecessarily large fat reserves that must be reduced prior to flight. 3. A second simulation model addresses foraging at sea by adults. This can produce the pattern of food provisioning observed at nests by assuming a random distribution of daily foraging success and that adults base their decision to continue foraging or return to the nest to feed their chick on the state of their own energy reserves. 4. Thus, these models relate the accumulation ot fat reserves in petrel chicks to stochastic variation in foraging experienced by individual birds rather than temporal variation in the feeding conditions for the population as a whole.