We propose a model of a capillary network in which chaotic capillary activity is crucial for efficient oxygenation of a muscle fiber. Tissue oxygenation by microcirculation is controlled by a complex pattern of opening and closing of precapillary sphincters, a phenomenon known as vasomotion. We model the individual precapillary sphincter as a non-linear oscillator that exhibits perfectly periodic vasomotion in isolation. The precapillary sphincters surrounding an active fiber are considered as a network; specific modes of interaction within this network result in complex patterns of vasomotion. In our model, efficient oxygenation of the fiber depends crucially on the mode of interaction among the vasomotions of the individual capillaries. Network interactions that lead to chaotic vasomotion are found to be essential for meeting the tissue oxygen demands precisely. Interactions that cause regular rhythmic patterns of vasomotion fail to meet oxygenation demands accurately. © 2007 Elsevier Inc. All rights reserved.