Neurons in auditory cortex of awake primates are selective for the spatial location of a sound source, yet the neural representation of the binaural cues that underlie this tuning remains undefined. We examined this representation in 283 single neurons across the low-frequency auditory core in alert macaques, trained to discriminate binaural cues for sound azimuth. In response to binaural beat stimuli, which mimic acoustic motion by modulating the relative phase of a tone at the two ears, these neurons robustly modulate their discharge rate in response to this directional cue. In accordance with prior studies, the preferred interaural phase difference (IPD) of these neurons typically corresponds to azimuthal locations contralateral to the recorded hemisphere. Whereas binaural beats evoke only transient discharges in anesthetized cortex, neurons in awake cortex respond throughout the IPD cycle. In this regard, responses are consistent with observations at earlier stations of the auditory pathway. Discharge rate is a bandpass function of the frequency of IPD modulation in most neurons (73%), but both discharge rate and temporal synchrony are independent of the direction of phase modulation. When subjected to a Receiver Operator Characteristic analysis, the responses of individual neurons are insufficient to account for the perceptual acuity of these macaques in an IPD discrimination task, suggesting the need for neural pooling at the cortical level.