The common marmoset (Callithrix jacchus) is a small New World primate that has increasingly been used as a non-human model in the fields of sensory, motor, and cognitive neuroscience. However, little knowledge exists regarding behavioral methods in this species. Developing an understanding of the neural basis of perception and cognition in an animal model requires measurement of both brain activity and behavior. Here we describe an operant conditioning behavioral training method developed to allow controlled psychoacoustic measurements in marmosets. We demonstrate that marmosets can be trained to consistently perform a Go/No-Go auditory task in which a subject licks at a feeding tube when it detects a sound. Correct responses result in delivery of a food reward. Crucially, this operant conditioning task generates little body movement and is well suited for pairing behavior with single-unit electrophysiology. Successful implementation of an operant conditioning behavior opens the door to a wide range of new studies in the field of auditory neuroscience using the marmoset as a model system.