We describe a simple computational model, based on generic features of cortical local circuits, that links cholinergic neuromodulation, gamma rhythmicity, and attentional selection. We propose that cholinergic modulation, by reducing adaptation currents in principal cells, induces a transition from asynchronous spontaneous activity to a "background" gamma rhythm (resembling the persistent gamma rhythms evoked in vitro by cholinergic agonists) in which individual principal cells participate infrequently and irregularly. We suggest that such rhythms accompany states of preparatory attention or vigilance and report simulations demonstrating that their presence can amplify stimulus-specific responses and enhance stimulus competition within a local circuit.