We speculate that sporadic apneas may be initiated and terminated by stochastic neural perturbations arising within or impinging upon the respiratory oscillator. A curious situation can then arise in which tiny perturbations that inhibit inspiration, paradoxically stimulate breathing. The plausibility of the hypothesis is supported by numerical analysis of a noisy attractor-cycle oscillator, and in studies of a preterm sleeping infant with sporadic apnea; low-level vibratory stimulation transformed the irregular apneic rhythm to eupnea.