We present a physiologically plausible binaural mechanism for the perception of the pitch of complex sounds via ghost stochastic resonance. In this scheme, two neurons are driven by noise and a different periodic signal each (with frequencies f(1)=kf(0) and f(2)=(k+1)f(0), where k>1), and their outputs (plus noise) are applied synaptically to a third neuron. Our numerical results, using the Morris-Lecar neuron model with chemical synapses explicitly considered, show that intermediate noise levels enhance the response of the third neuron at frequencies close to f(0), as in the cases previously described of ghost resonance. For the case of an inharmonic combination of inputs (f(1)=kf(0)+Deltaf and f(2)=(k+1)f(0)+Deltaf) noise is also seen to enhance the rates of most probable spiking for the third neuron at a frequency f(r)=f(0)+[Deltaf(k+12)]. In addition, we show that similar resonances can be observed as a function of the synaptic time constant. The suggested ghost-resonance-based stochastic mechanism can thus arise either at the peripheral level or at a higher level of neural processing in the perception of pitch.