Auditory sound source localization with only two ears is a computationally intensive problem. Nevertheless, some animals show impressive performance solving it. Neurons in the auditory system of these animals are specialized to exploit spatial information from binaural sound signals. A set of neurons located in the lateral superior olivary (LSO) complex responds to interaural level differences. Here, we present a spike-based sound source localization model inspired by neurons in the LSO that computes the level difference of incoming spike signals by integrating excitatory and inhibitory inputs for localizing sound sources. The model is implemented on the IBM TrueNorth neurosynaptic system to achieve real-time compute performance. We introduce system components, like spectro-temporal smoothing and weighted sum units and explain how they are implemented on the TrueNorth chip. Correct behavior for synthetic inputs is demonstrated. Finally, test scenarios with recorded natural sounds indicate that the system reliably computes the interaural level difference of perceived sound sources.