Binaural acoustic source localization is important to human listeners for spatial awareness, communication and safety. In this paper, an end-to-end binaural localization model for speech in noise is presented. A lightweight convolutional recurrent network that localizes sound in the frontal azimuthal plane for noisy reverberant binaural signals is introduced. The model incorporates additive internal ear noise to represent the frequency-dependent hearing threshold of a typical listener. The localization performance of the model is compared with the steered response power algorithm, and the use of the model as a measure of interaural cue preservation for binaural speech enhancement methods is studied. A listening test was performed to compare the performance of the model with human localization of speech in noisy conditions.