Improving the intelligibility of speech in different environments is one of the main objectives of hearing aid signal processing algorithms. Hearing aids typically employ beamforming techniques using multiple microphones for this task. In this paper, we discuss a binaural beamforming scheme that uses signals from the hearing aids worn on both the left and right ears. Specifically, we analyze the effect of a low bit rate wireless communication link between the left and right hearing aids on the performance of the beamformer. The scheme is comprised of a generalized sidelobe canceller (GSC) that has two inputs: observations from one ear, and quantized observations from the other ear, and whose output is an estimate of the desired signal. We analyze the performance of this scheme in the presence of a localized interferer as a function of the communication bit rate using the resultant mean-squared error as the signal distortion measure.